A131802 Sequence related to factorizations and prime signatures: a(1) = 1; for n>1, a(n) = A057567(n) - 2*A001055(n).

1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 1, 2, 0, 3, 0, 3, 1, 1, 0, 7, 0, 1, 1, 3, 0, 5, 0, 5, 1, 1, 1, 8, 0, 1, 1, 7, 0, 5, 0, 3, 3, 1, 0, 14, 0, 3, 1, 3, 0, 7, 1, 7, 1, 1, 0, 14, 0, 1, 3, 8, 1, 5, 0, 3, 1, 5, 0, 20, 0, 1, 3, 3, 1, 5, 0, 14, 2, 1, 0, 14, 1, 1, 1, 7

Offset: 1

Author

Alford Arnold, Jul 18 2007

Keywords

• easy
• nonn

Examples

			A001055(12) = 4 and A057567(12) = 11 so a(12) = 11 - 2*4 = 3
		

Links

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

Crossrefs

Cf. A001055, A025487, A057567, A077569, A108464, A122819.

Programs

PARI

fcnt(n, m) = {local(s); s=0; if(n == 1, s=1, fordiv(n, d, if(d > 1 & d <= m, s=s+fcnt(n/d, d)))); s}
A001055(n) = fcnt(n, n) \\ This function from Michael B. Porter, Oct 29 2009
A057567(n) = sumdiv(n, d, A001055(d));
A131802(n) = if(1==n,n,A057567(n) - 2*A001055(n)); \\ Antti Karttunen, May 25 2017