A334734 -id:A334734 - cp's OEIS frontend

A166604 Numbers k such that Sum_{i=1..k} i^4 divides Product_{i=1..k} i^4.

1, 31, 59, 94, 104, 122, 133, 181, 206, 223, 244, 248, 283, 298, 318, 342, 356, 401, 406, 421, 422, 439, 444, 449, 451, 469, 479, 493, 496, 507, 528, 532, 536, 541, 555, 597, 631, 637, 643, 668, 701, 706, 712, 717, 721, 722, 754, 762, 795, 797, 801, 815, 842

Offset: 1

Alexander Adamchuk, Oct 18 2009

nonn

			a(2) = A125314(4) = 31.

Harvey P. Dale, Table of n, a(n) for n = 1..3000

Cf. A125314, A166602, A060462, A166605, A166606, A166607, A166608, A166609, A166610, A181426, A334734.

k = s = 1; p = 1; lst = {}; While[k < 1000, If[ Mod[p, s] == 0, AppendTo[lst, k]]; k++; s = s + k^4; p = p*k^4]; lst (* Robert G. Wilson v, Nov 02 2009 *)
Module[{nn=1000,c},c=Range[nn]^4;Select[Range[nn],Divisible[Times@@ Take[ c,#], Total[Take[c,#]]]&]] (* Harvey P. Dale, Dec 18 2013 *)

a(15)-a(53) from Robert G. Wilson v, Nov 02 2009

A181426 Numerator of Sum_{k=1..n} k^4 / Product_{k=1..n} k^4.

Original entry on oeis.org

1, 17, 49, 59, 979, 91, 167, 731, 5111, 517, 1817, 6071, 109, 18241, 22289, 2771, 131, 28823, 67, 51619, 11911, 34891, 15557, 257, 1949, 22313, 2267, 14123, 153931, 5273999, 1, 3167, 45091, 3569, 268309, 126947, 4217, 127, 369641, 201679, 85739

Offset: 1

Alexander Adamchuk, Oct 18 2010

a(n) = 1 for n = {1, 31, 59, 94, 104, 122, 133, 181, 206, 223, ...} = A166604.

			The first few fractions are 1, 17/16, 49/648, 59/55296, 979/207360000, 91/10749542400, 167/23044331520000, ... = A181426/A334734.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A090585 = Numerator of Sum/Product of first n numbers.
Cf. A125294 = Numerator of Sum/Product of squares of first n numbers.
Cf. A166604, A334734 (denominators).

Table[Numerator[Sum[ k^4, {k, 1, n}] / Product[k^4, {k, 1, n}]], {n, 1, 100}]
With[{c=Range[50]^4},Numerator[Accumulate[c]/FoldList[Times,c]]] (* Harvey P. Dale, Jul 03 2025 *)

a(n) = numerator(sum(k=1, n, k^4)/prod(k=1, n, k^4)); \\ Michel Marcus, May 09 2020

cp's OEIS Frontend

A166604 Numbers k such that Sum_{i=1..k} i^4 divides Product_{i=1..k} i^4.

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