A336455 a(n) = A335915(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, 1, 3, 1, 1, 1, 3, 21, 1, 1, 3, 3, 1, 1, 15, 1, 21, 3, 3, 1, 1, 1, 3, 15, 3, 3, 3, 3, 1, 1, 3, 1, 1, 1, 63, 45, 3, 3, 3, 3, 1, 15, 3, 21, 1, 1, 15, 45, 15, 1, 9, 1, 3, 1, 3, 3, 3, 3, 3, 15, 1, 21, 63, 3, 1, 9, 3, 1, 1, 1, 63, 171, 45, 15, 9, 1, 3, 3, 15, 225, 3, 3, 3, 1, 15, 3, 3, 3, 21, 3, 3, 1, 1, 3, 3, 9, 45, 21, 45

Offset

1,4

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(n)).

Multiplicative with a(p^e) = A335915(1 + p + p^2 + ... + p^e).

a(A000203(n)) = A336456(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]))); };
A336455(n) = A335915(sigma(n));
\\ Alternatively, as:
A336455(n) =  { my(f=factor(n)); prod(k=1, #f~, A335915(((f[k, 1]^(1+f[k, 2]))-1)/(f[k, 1]-1))); };

Crossrefs

Cf. A000265, A000203, A335915, A336456.

Cf. also A336461, A336462, A336464.

Sequence in context: A323840 A195644 A143632 * A388403 A130605 A354872

Adjacent sequences: A336452 A336453 A336454 * A336456 A336457 A336458

Keyword

nonn,mult

Author

Antti Karttunen, Jul 22 2020

Status

approved