A343440 a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * 2^(d-1).

1, 1, 3, 7, 15, 27, 63, 127, 255, 495, 1023, 2037, 4095, 8127, 16365, 32767, 65535, 130815, 262143, 524265, 1048509, 2096127, 4194303, 8388477, 16777215, 33550335, 67108863, 134217657, 268435455, 536854005, 1073741823, 2147483647, 4294966269, 8589869055, 17179869105

Offset

1,3

Links

Table of n, a(n) for n=1..35.

Formula

a(n) = 2^(n-1) - Sum_{d|n, gcd(d, n/d) = 1, d < n} a(d).

Mathematica

a[n_] := Sum[If[GCD[d, n/d] == 1, (-1)^PrimeNu[n/d] 2^(d - 1), 0], {d, Divisors[n]}]; Table[a[n], {n, 35}]

Prog

(PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d)==1, (-1)^omega(n/d) * 2^(d-1))); \\ Michel Marcus, Apr 15 2021

Crossrefs

Cf. A000740, A001221, A011782, A076479.

Sequence in context: A139806 A143701 A147638 * A147394 A350370 A103021

Adjacent sequences: A343437 A343438 A343439 * A343441 A343442 A343443

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 15 2021

Status

approved