A329891 a(0) = 0, a(1) = 1, for n > 1, a(n) = 2^n - (sigma((2^n)-1) - sigma((2^(n-1))-1)).

0, 1, 1, 4, 0, 24, -8, 104, -48, 352, 80, 1424, -2480, 8736, 2048, 16384, -7008, 111456, -80384, 473600, -427008, 1630976, 750592, 5731232, -12709664, 36894720, 12300416, 68246368, -38345568, 459223232, -401666240, 2015330304, -862152384, 5535523520, 4631692288, 21015756800, -61319782400, 165674113600, 46426506688, 279934140416, -484569911296

Offset: 0

Author

Antti Karttunen, Nov 23 2019

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 0..255
• Index entries for sequences related to sigma(n)

Crossrefs

Row 1 of A329637.

Cf. A000203, A000225, A075708, A156552, A323243, A323244, A329644, A329890, A329892.

Programs

PARI

A329891(n) = if(n<=1,n,(2^n - sigma((2^n)-1)) + sigma((2^(n-1))-1));

Formula

a(0) = 0; for n >= 1, a(n) = A323244(2^n) - A323244(2^(n-1)) = 2^n - A329890(n).

a(n) = A329644(2^n).