A323174 Deficiency computed for conjugated prime factorization: a(n) = A033879(A122111(n)).

1, 1, 1, 2, 1, 0, 1, 4, 5, -4, 1, 2, 1, -12, -3, 6, 1, 6, 1, -2, -19, -28, 1, 4, 14, -60, 19, -10, 1, -12, 1, 10, -51, -124, -12, 10, 1, -252, -115, 0, 1, -48, 1, -26, 7, -508, 1, 8, 41, 12, -243, -58, 1, 22, -64, -8, -499, -1020, 1, -12, 1, -2044, -17, 12, -168, -120, 1, -122, -1011, -54, 1, 18, 1, -4092, 26, -250, -39, -264, 1, 4

Offset: 1

Author

Antti Karttunen, Jan 10 2019

Keywords

• sign

Comments

Zeros occur at A122111(A000396(k)), k >= 1: 6, 40, 11264, 18253611008, ...

Links

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

Crossrefs

Cf. A033879, A122111, A323167, A323168.

Cf. also A323244.

Programs

Mathematica

A122111[n_] := Product[Prime[Sum[If[jA122111[n]}, 2k - DivisorSigma[1, k]];
Array[a, 80] (* Jean-François Alcover, Sep 23 2020 *)

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)));
A323174(n) = { my(k=A122111(n)); ((2*k)-sigma(k)); }

Formula

a(n) = A033879(A122111(n)).

a(n) = 2*A122111(n) - A323173(n).