A329890 a(1) = 1; for n > 1, a(n) = sigma((2^n)-1) - sigma((2^(n-1))-1), where sigma is A000203, the sum of divisors.

1, 3, 4, 16, 8, 72, 24, 304, 160, 944, 624, 6576, -544, 14336, 16384, 72544, 19616, 342528, 50688, 1475584, 466176, 3443712, 2657376, 29486880, -3340288, 54808448, 65971360, 306781024, 77647680, 1475408064, 132153344, 5157119680, 3054411072, 12548176896, 13343981568, 130039259136, -28235160128, 228451400256, 269821673472

Offset: 1

Author

Antti Karttunen, Dec 08 2019

Keywords

• sign

Links

• Index entries for sequences related to sigma(n)

Crossrefs

From second term onwards, the first differences of A075708.

Cf. A000203, A329637, A329891, A329892.

Programs

Mathematica

Join[{1},Table[DivisorSigma[1,2^n-1]-DivisorSigma[1,2^(n-1)-1],{n,2,40}]] (* Harvey P. Dale, Aug 18 2024 *)

PARI

A329890(n) = if(1==n,1,sigma((2^n)-1)-sigma((2^(n-1))-1));

Formula

a(1) = 1; and for n > 1, a(n) = A075708(n) - A075708(n-1).