A336459 a(n) = A065330(sigma(sigma(n))), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.

1, 1, 7, 1, 1, 7, 5, 1, 7, 13, 7, 7, 1, 5, 5, 1, 13, 7, 7, 1, 7, 91, 5, 7, 1, 1, 5, 5, 1, 65, 7, 13, 31, 5, 31, 7, 5, 7, 5, 13, 1, 7, 7, 7, 7, 65, 31, 7, 5, 1, 65, 19, 5, 5, 65, 5, 31, 13, 7, 5, 1, 7, 35, 1, 7, 403, 7, 13, 7, 403, 65, 7, 19, 5, 7, 7, 7, 5, 31, 1, 133, 13, 7, 7, 35, 7, 5, 91, 13, 91, 31, 5, 85, 403

Offset

1,3

Comments

Sequence removes prime factors 2 and 3 from the prime factorization A051027(n) = sigma(sigma(n)).

Like A051027, neither this is multiplicative. For example, we have a(3) = 7, a(7) = 5, but a(21) = 7 <> 35. However, for example, a(10) = 13, and a(3*10) = a(3)*a(10) = 65.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences related to sigma(n)

Formula

a(n) = A336457(A000203(n)) = A065330(A051027(n)).

Prog

(PARI)
A065330(n) = (n>>valuation(n, 2)/3^valuation(n, 3));
A336459(n) = A065330(sigma(sigma(n)));

Crossrefs

Cf. A000203, A051027, A065330, A336456 (similar sequence), A336457.

Cf. also A336561 (positions where this appears to be multiplicative but A051027 does not).

Sequence in context: A019620 A105395 A120437 * A367764 A174095 A305607

Adjacent sequences: A336456 A336457 A336458 * A336460 A336461 A336462

Keyword

nonn

Author

Antti Karttunen, Jul 25 2020

Status

approved