A318470 Multiplicative with a(p^e) = A260443(e).

1, 2, 2, 3, 2, 4, 2, 6, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 12, 3, 4, 6, 6, 2, 8, 2, 18, 4, 4, 4, 9, 2, 4, 4, 12, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 12, 4, 12, 4, 4, 2, 12, 2, 4, 6, 15, 4, 8, 2, 6, 4, 8, 2, 18, 2, 4, 6, 6, 4, 8, 2, 10, 5, 4, 2, 12, 4, 4, 4, 12, 2, 12, 4, 6, 4, 4, 4, 36, 2, 6, 6, 9, 2, 8, 2, 12, 8

Offset: 1

Author

Antti Karttunen, Aug 30 2018

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A260443, A318306, A318307.

Differs from A293442 for the first time at n=32, where a(32) = 18, while A293442(32) = 10.

Cf. also A293216, A293217, A293443, A318469.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2))));
A318470(n) = factorback(apply(e -> A260443(e),factor(n)[,2]));

Formula

For all n >= 1, A001222(a(n)) = A318306(n).