A323167 a(n) = A294898(A122111(n)).

0, 0, 0, 0, 0, -2, 0, 2, 3, -6, 0, 0, 0, -14, -5, 3, 0, 2, 0, -4, -21, -30, 0, 1, 10, -62, 16, -12, 0, -16, 0, 7, -53, -126, -16, 7, 0, -254, -117, -3, 0, -52, 0, -28, 4, -510, 0, 5, 38, 8, -245, -60, 0, 19, -68, -11, -501, -1022, 0, -15, 0, -2046, -20, 9, -172, -124, 0, -124, -1013, -58, 0, 16, 0, -4094, 22, -252, -42, -268, 0, 1, 38

Offset: 1

Author

Antti Karttunen, Jan 10 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A005187, A294898, A122111, A322867, A323174, A323168.

Cf. also A295296, A323248.

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)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A294898(n) = (A005187(n)-sigma(n));
A323167(n) = A294898(A122111(n));
\\ Or alternatively as:
A322867(n) = hammingweight(A122111(n));
A323174(n) = { my(k=A122111(n)); ((2*k)-sigma(k)); }
A323167(n) = (A323174(n) - A322867(n));

Formula

a(n) = A294898(A122111(n)).

a(n) = A323174(n) - A322867(n).