A335915 Fully multiplicative with a(2) = 1, and a(p) = A000265(p-1)*A000265(p+1) = A000265(p^2 - 1), for odd primes p.

1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 15, 1, 21, 3, 3, 1, 9, 1, 45, 3, 3, 15, 33, 1, 9, 21, 1, 3, 105, 3, 15, 1, 15, 9, 9, 1, 171, 45, 21, 3, 105, 3, 231, 15, 3, 33, 69, 1, 9, 9, 9, 21, 351, 1, 45, 3, 45, 105, 435, 3, 465, 15, 3, 1, 63, 15, 561, 9, 33, 9, 315, 1, 333, 171, 9, 45, 45, 21, 195, 3, 1, 105, 861, 3, 27, 231, 105, 15, 495, 3, 63, 33, 15, 69

Offset

1,5

Comments

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A336118(i) = A336118(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..8192

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

Formula

Completely multiplicative with a(2) = 1, and for odd primes p, a(p) = A000265(p-1)*A000265(p+1).

For all n >= 1, A335904(a(n)) = A336118(n).

For all n >= 0, a(2^n) = a(3^n) = 1, a(5^n) = a(7^n) = 3^n.

a(n) = A336466(n) * A336467(n). - Antti Karttunen, Jan 31 2021

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]-1)*A000265(f[k, 1]+1))^f[k, 2])); };

Crossrefs

Cf. A000265.

Cf. also A167344, A324400, A335904, A336118, A336455, A336456, A336466, A336467.

Sequence in context: A098877 A225212 A091088 * A249781 A342041 A115627

Adjacent sequences: A335912 A335913 A335914 * A335916 A335917 A335918

Keyword

nonn,mult,look

Author

Antti Karttunen, Jul 09 2020

Status

approved