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A309083
a(n) = n - floor(n/2^4) + floor(n/3^4) - floor(n/4^4) + ...
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 11 2019
STATUS
approved