A324117 Number of odd divisors in A156552(n): a(1) = 0, for n > 1, a(n) = A001227(A156552(n)) = A000005(A322993(n)).

0, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 3, 4, 1, 2, 2, 4, 2, 4, 1, 4, 1, 2, 2, 4, 2, 4, 1, 2, 4, 4, 1, 2, 1, 2, 2, 8, 1, 2, 2, 3, 4, 2, 1, 2, 3, 2, 4, 6, 1, 2, 1, 4, 2, 6, 2, 4, 1, 4, 2, 2, 1, 4, 1, 4, 2, 4, 2, 4, 1, 2, 4, 4, 1, 6, 4, 8, 8, 8, 1, 6, 3, 4, 6, 12, 4, 4, 1, 3, 4, 4, 1, 6, 1, 2, 4

Offset: 1

Author

Antti Karttunen, Feb 20 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4473
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A001227, A156552, A246277, A322813, A322993, A324105, A324115, A324118.

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));
A246277(n) = { if(1==n, 0, while((n%2), n = A064989(n)); (n/2)); };
A322993(n) = A156552(2*A246277(n));
A324117(n) = if(1==n, 0, numdiv(A322993(n)));

Formula

a(1) = 0; for n > 1, a(n) = A000005(A322993(n)) = A000005(A156552(2*A246277(n))) = A324105(2*A246277(n)).