A324115 a(n) = A002487(A323244(n)).

0, 1, 1, 1, 1, 1, 1, 2, 0, 3, 1, 3, 1, 1, 1, 2, 1, 2, 1, 4, -2, 4, 1, 5, -1, 7, 1, 5, 1, 3, 1, 4, 3, 11, -1, 3, 1, 1, -2, 5, 1, 4, 1, 6, 1, 13, 1, 7, -2, 7, 1, 7, 1, 3, -7, 9, -2, 25, 1, 8, 1, 76, 1, 5, 3, 8, 1, 21, 7, 3, 1, 7, 1, 31, 3, 31, -3, 13, 1, 10, -2, 199, 1, 5, -4, 101, -18, 4, 1, 2, -12, 43, 11, 266, -5, 9, 1, 11, -1, 4, 1, 6, 1, 13

Offset: 1

Author

Antti Karttunen, Feb 20 2019

Keywords

• sign

Comments

If there are no odd perfect numbers then A324201 gives the positions of all zeros after the initial a(1) = 0.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4473

Crossrefs

Cf. A002487, A033879, A156552, A323244, A323902, A324201, A324116, A324117.

Programs

PARI

A002487(n) = if(abs(n)<=1, n, A002487(n\2) + if( n%2, A002487(n\2 + 1))); \\ This version works consistently also with negative arguments, so that a(-n) = -a(n). Except that it is very slow on large n.
A002487(n) = { my(s=sign(n), a=1, b=0); n = abs(n); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (s*b); }; \\ So we use this one, modified from the one given in A002487
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))));
A323244(n) = if(1==n, 0, my(k=A156552(n)); (2*k)-sigma(k));
A324115(n) = A002487(A323244(n));

Formula

a(n) = A002487(A323244(n)), with the definition of A002487 extended to the negative arguments so that A002487(-n) = -A002487(n).

a(A324201(n)) = 0.