A319994 - OEIS

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A319994

Let g = A006530(n), the largest prime factor of n. This filter sequence combines (g mod 4), n/g (A052126), and a single bit A319988(n) telling whether the largest prime factor is unitary.

1, 2, 3, 4, 5, 6, 3, 7, 8, 9, 3, 10, 5, 6, 11, 12, 5, 13, 3, 14, 15, 6, 3, 16, 17, 9, 18, 10, 5, 19, 3, 20, 15, 9, 21, 22, 5, 6, 11, 23, 5, 24, 3, 10, 25, 6, 3, 26, 27, 28, 11, 14, 5, 29, 21, 16, 15, 9, 3, 30, 5, 6, 31, 32, 33, 24, 3, 14, 15, 34, 3, 35, 5, 9, 36, 10, 37, 19, 3, 38, 39, 9, 3, 40, 33, 6, 11, 16, 5, 41, 42, 10, 15, 6, 21, 43, 5, 44, 31, 45, 5, 19, 3, 23, 46

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Restricted growth sequence transform of triple [A010873(A006530(n)), A052126(n), A319988(n)], with a separate value allotted for a(1).

Here among the first 100000 terms, only 2331 have a unique value, compared to 69714 in A320004.

For all i, j:

a(i) = a(j) => A024362(i) = A024362(j),

a(i) = a(j) => A067029(i) = A067029(j),

a(i) = a(j) => A071178(i) = A071178(j),

a(i) = a(j) => A077462(i) = A077462(j) => A101296(i) = A101296(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 100000;

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; };

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);

A052126(n) = (n/A006530(n));

A319988(n) = ((n>1)&&(factor(n)[omega(n), 2]>1));

A319994aux(n) = if(1==n, 0, [A006530(n)%4, A052126(n), A319988(n)]);

v319994 = rgs_transform(vector(up_to, n, A319994aux(n)));

A319994(n) = v319994[n];

CROSSREFS

Cf. A006530, A052126, A319988, A320004.

Cf. also A319996 (modulo 6 analog).

Sequence in context: A274630 A278058 A320115 * A319714 A320004 A319704

Adjacent sequences: A319991 A319992 A319993 * A319995 A319996 A319997

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 05 2018

STATUS

approved