The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A319347

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A319347

Filter sequence combining A000035(n) (parity of n), A003557(n), and A046523(n) (prime signature of n).
(history; published version)

#9 by N. J. A. Sloane at Sat Jan 19 04:15:43 EST 2019

COMMENTS

Restricted growth sequence transform of triplet triple [A000035(n), A003557(n), A046523(n)], or equally, of triplet triple [A007814(n), A003557(n), A046523(n)], or equally, of ordered pair [A000035(n), A291757(n)].

Discussion

Sat Jan 19

04:15

OEIS Server: https://oeis.org/edit/global/2799

#8 by Susanna Cuyler at Mon Sep 24 17:46:44 EDT 2018

STATUS

proposed

approved

#7 by Antti Karttunen at Mon Sep 24 13:02:25 EDT 2018

STATUS

editing

proposed

#6 by Antti Karttunen at Mon Sep 24 13:01:59 EDT 2018

PROG

A007814(n) = valuation(n, 2);

#5 by Antti Karttunen at Mon Sep 24 13:01:01 EDT 2018

NAME

Filter sequence combining A000035 (n) (parity of n), A003557(n), and A046523(n) (prime signature of n).

#4 by Antti Karttunen at Mon Sep 24 13:00:41 EDT 2018

NAME

Filter sequence combining A000035 (parity of n), A003557(n), A007814(n) and A046523(n) (prime signature of n).

#3 by Antti Karttunen at Mon Sep 24 12:45:05 EDT 2018

COMMENTS

For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A305891(i) = A305891(j).

LINKS

Antti Karttunen, <a href="/A319347/b319347.txt">Table of n, a(n) for n = 1..65537</a>

CROSSREFS

Cf. A000035, A003557, A007814, A046523, A291757, A305801, A305891.

#2 by Antti Karttunen at Mon Sep 24 12:39:23 EDT 2018

NAME

allocated for Antti KarttunenFilter sequence combining A003557(n), A007814(n) and A046523(n).

DATA

1, 2, 3, 4, 3, 5, 3, 6, 7, 5, 3, 8, 3, 5, 9, 10, 3, 11, 3, 8, 9, 5, 3, 12, 13, 5, 14, 8, 3, 15, 3, 16, 9, 5, 9, 17, 3, 5, 9, 12, 3, 15, 3, 8, 18, 5, 3, 19, 20, 21, 9, 8, 3, 22, 9, 12, 9, 5, 3, 23, 3, 5, 18, 24, 9, 15, 3, 8, 9, 15, 3, 25, 3, 5, 26, 8, 9, 15, 3, 19, 27, 5, 3, 23, 9, 5, 9, 12, 3, 28, 9, 8, 9, 5, 9, 29, 3, 30, 18, 31, 3, 15, 3, 12, 32

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of triplet [A000035(n), A003557(n), A046523(n)], or equally, of triplet [A007814(n), A003557(n), A046523(n)], or equally, of ordered pair [A000035(n), A291757(n)].

PROG

(PARI)

up_to = 65537;

rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };

A007814(n) = valuation(n, 2);

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p=0); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };

v319347 = rgs_transform(vector(up_to, n, [A003557(n), (n%2), A046523(n)]));

A319347(n) = v319347[n];

CROSSREFS

Cf. A000035, A003557, A007814, A046523, A291757, A305801,

KEYWORD

allocated

nonn

AUTHOR

Antti Karttunen, Sep 24 2018

STATUS

approved

editing

#1 by Antti Karttunen at Mon Sep 17 07:59:04 EDT 2018

NAME

allocated for Antti Karttunen

KEYWORD

allocated

STATUS

approved