A279487 -id:A279487 - cp's OEIS frontend

A276517 Indices k such that A276516(k) = 0.

2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 41, 43, 44, 45, 46, 47, 48, 53, 54, 60, 61, 67, 70, 72, 74, 76, 79, 82, 84, 87, 90, 92, 93, 96, 105, 106, 107, 108, 111, 112, 114, 117, 122, 128, 133, 135, 139, 141, 148, 159

Offset: 1

Vaclav Kotesovec, Dec 12 2016

nonn

This is different from A001422, first difference: a(14) = 25, A001422(14) = 27.

Conjecture: for k > 7169 there are no more terms in this sequence (tested for k < 10000000).

			3 is in the sequence because A276516(3) = 0
4 is not in the sequence because A276516(4) = -1
4222 is in the sequence because A276516(4222) = 0
7169 is in the sequence because A276516(7169) = 0

Vaclav Kotesovec, Table of n, a(n) for n = 1..173

Cf. A001422, A001661, A276516, A279486, A279487.

nn = 100; A276516 = Rest[CoefficientList[Series[Product[(1-x^(k^2)), {k, nn}], {x, 0, nn^2}], x]]; Select[Range[nn^2], A276516[[#]]==0&]
nmax = 10000; nn = Floor[Sqrt[nmax]]+1; poly = ConstantArray[0, nn^2 + 1]; poly[[1]] = 1; poly[[2]] = -1; poly[[3]] = 0; Do[Do[poly[[j + 1]] -= poly[[j - k^2 + 1]], {j, nn^2, k^2, -1}];, {k, 2, nn}]; A276516 = Take[poly, {2, nmax+1}]; Select[Range[nmax], A276516[[#]]==0&]

A046039 Numbers which cannot be represented as a sum of distinct 4th powers.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Eric W. Weisstein

Last term is a(889576) = 5134240. [Charles R Greathouse IV, Feb 26 2012]

Vaclav Kotesovec, Table of n, a(n) for n = 1..60000
Eric Weisstein's World of Mathematics, Biquadratic Number

Cf. A001422, A001476. Complement of A003999.

Cf. A279487.

max = 2000; f[x_] := Product[1 + x^(k^4), {k, 1, 10}]; A003999 = Exponent[#, x]& /@ List @@ Normal[Series[f[x], {x, 0, max}]] // Rest; A046039 = Complement[Range[max], A003999][[1 ;; 71]](* Jean-François Alcover, Nov 09 2012, after Charles R Greathouse IV *)

select( is_A046039(n,m=n)={m^4>n&& m=sqrtnint(n,4); n!=m^4&& !while(m>1, is_A046039(n-m^4, m--)||return)}, [1..74]) \\ M. F. Hasler, Apr 21 2020

A279529 a(n) is a largest m such that coefficient [x^m] in Product_{k>=1} (1-x^(k^n)) is equal to zero.

Original entry on oeis.org

7169, 353684, 64674419

Offset: 2

Vaclav Kotesovec, Dec 14 2016

			a(2) = 7169 because A276516(7169) = 0 and A276516(m) <> 0 for m > 7169.
a(3) = 353684 because A279484(353684) = 0 and A279484(m) <> 0 for m > 353684.
a(4) = 64674419 because A279485(64674419) = 0 and A279485(m) <> 0 for m > 64674419.
a(2) = A276517(173) = 7169.
a(3) = A279486(5216) = 353684.
a(4) = A279487(1040799) = 64674419.

Cf. A001661.
Cf. A276517, A279486, A279487.
Cf. A276516, A279484, A279485.
Cf. A001422, A001476, A046039.

cp's OEIS Frontend

A276517 Indices k such that A276516(k) = 0.

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A046039 Numbers which cannot be represented as a sum of distinct 4th powers.

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Mathematica

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A279529 a(n) is a largest m such that coefficient [x^m] in Product_{k>=1} (1-x^(k^n)) is equal to zero.

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