A353521 - OEIS

A353521

Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A000035(i) = A000035(j), for all i, j >= 1.

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 22, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 53, 54, 55, 47, 56, 3, 57, 58, 59, 3, 60, 42, 61, 62, 63, 3, 64, 38

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A000035(n)].

For all i, j:

A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),

a(i) = a(j) => A007814(i) = A007814(j),

a(i) = a(j) => A344025(i) = A344025(j),

a(i) = a(j) => A353522(i) = A353522(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

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; };

A000035(n) = (n%2);

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A003557(n) = (n/factorback(factorint(n)[, 1]));

Aux353521(n) = [A003415(n), A003557(n), A000035(n)];

v353521 = rgs_transform(vector(up_to, n, Aux353521(n)));

A353521(n) = v353521[n];

CROSSREFS

Cf. A000035, A003415, A003557, A007814.

Cf. also A305801, A344025, A351260, A353520, A353522.

Sequence in context: A323367 A323370 A323405 * A319349 A373981 A353520

Adjacent sequences: A353518 A353519 A353520 * A353522 A353523 A353524

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 27 2022

STATUS

approved