A309083 a(n) = n - floor(n/2^4) + floor(n/3^4) - floor(n/4^4) + ...

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

G.f.: (1/(1 - x)) * Sum_{k>=1} (-1)^(k+1) * x^(k^4)/(1 - x^(k^4)).

a(n) ~ 7*zeta(4)*n/8 = 7*Pi^4*n/720. - Vaclav Kotesovec, Oct 12 2019

Mathematica

Table[Sum[(-1)^(k + 1) Floor[n/k^4], {k, 1, n}], {n, 1, 75}]
nmax = 75; CoefficientList[Series[1/(1 - x) Sum[(-1)^(k + 1) x^(k^4)/(1 - x^(k^4)), {k, 1, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x] // Rest
Table[Sum[Boole[IntegerQ[d^(1/4)] && OddQ[d]], {d, Divisors[n]}] - Sum[Boole[IntegerQ[d^(1/4)] && EvenQ[d]], {d, Divisors[n]}], {n, 1, 75}] // Accumulate

Crossrefs

Cf. A013938, A059851, A063775, A309081, A309082.

Sequence in context: A117657 A352529 A357434 * A106618 A320113 A080684

Adjacent sequences: A309080 A309081 A309082 * A309084 A309085 A309086

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 11 2019

Status

approved