A336456 a(n) = A335915(sigma(sigma(n))), where A335915 is a fully multiplicative sequence with a(2) = 1 and a(p) = A000265(p^2 - 1) for odd primes p, with A000265(k) giving the odd part of k.

1, 1, 3, 1, 1, 3, 3, 1, 3, 21, 3, 3, 1, 3, 3, 1, 21, 3, 3, 1, 3, 63, 3, 3, 1, 1, 3, 3, 1, 63, 3, 21, 15, 3, 15, 3, 3, 3, 3, 21, 1, 3, 3, 3, 3, 63, 15, 3, 3, 1, 63, 45, 3, 3, 63, 3, 15, 21, 3, 3, 1, 3, 9, 1, 3, 315, 3, 21, 3, 315, 63, 3, 45, 3, 3, 3, 3, 3, 15, 1, 135, 21, 3, 3, 9, 3, 3, 63, 21, 63, 15, 3, 27, 315

Offset

1,3

Comments

Like A051027, neither this is multiplicative. For example, we have a(3) = 3, a(7) = 3, but a(21) = 3 <> 9. However, for example, a(10) = 21, and a(3*10) = 63.

Links

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

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

Formula

a(n) = A335915(A000203(A000203(n))) = A336455(A000203(n)) = A335915(A051027(n)).

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A335915(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265((f[k, 1]^2)-1)^f[k, 2]))); };
A336456(n) = A335915(sigma(sigma(n)));

Crossrefs

Cf. A000203, A051027, A335915.

Cf. also A336462, A336463, A336464.

Sequence in context: A091442 A025834 A257379 * A227898 A035649 A278509

Adjacent sequences: A336453 A336454 A336455 * A336457 A336458 A336459

Keyword

nonn

Author

Antti Karttunen, Jul 22 2020

Status

approved