A353757 a(n) = A353750(n) - A353749(n).

0, 3, -2, 28, -8, 4, -26, 44, 108, 12, -62, 52, -102, -14, -32, 862, -184, 504, -282, 96, -104, -22, -402, 80, 690, -12, -96, 60, -596, 48, -854, 704, -248, -64, -328, 3912, -810, -210, -408, 240, -1360, -56, -1582, 100, 240, -322, -1946, 1708, 174, 3300, -736, 786, -2300, 48, -744, 72, -1128, -356, -2978, 384

Offset: 1

Author

Antti Karttunen, May 10 2022

Keywords

• sign

Comments

It is conjectured that there are no other zeros after a(1) = 0.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A064989, A353749, A353750, A353758 (positions of negative terms), A353759 (of terms >= 0), A353760.

Cf. also A348736.

Programs

PARI

A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A353749(n) = (eulerphi(n)*A064989(n));
A353757(n) = { my(s=sigma(n)); (A353749(s)-A353749(n)); };

Formula

a(n) = A353750(n) - A353749(n) = A353749(A000203(n)) - A353749(n).