A329892 a(0) = 0, a(1) = 1, for n > 1, a(n) = 2^(n+1) - 3*(sigma((2^n)-1) - sigma((2^(n-1))-1)).

0, 1, -1, 4, -16, 40, -88, 184, -400, 544, -784, 2224, -11536, 18016, -10240, 16384, -86560, 203296, -503296, 896512, -2329600, 2795776, -1942528, 8805088, -54906208, 77129728, -30207616, 70521376, -383472160, 840798784, -2278740544, 3898507264, -6881424448, 8016635968, -3284792320, 28687532032, -252678823936, 359583387328, -135598386880

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 2 of A329637.

Cf. A000203, A000225, A075708, A156552, A323243, A329644, A329890, A329891.

Programs

PARI

A329890(n) = if(1==n,1,sigma((2^n)-1)-sigma((2^(n-1))-1));
A329892(n) = if(!n,n,2^(n+1) - 3*A329890(n));

PARI

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A323243(n) = if(1==n, 0, sigma(A156552(n)));
A329644(n) = sumdiv(n, d, moebius(n/d)*((2*A156552(d))-A323243(d)));
A329892(n) = A329644(3^n);

Formula

a(n) = A329644(3^n).

a(0) = 0; for n >= 1, a(n) = 2^(n+1) - 3*A329890(n).