A078132 -id:A078132 - cp's OEIS frontend

A078128 Number of ways to write n as sum of cubes > 1.

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 1, 0, 2, 1

Offset: 1

Reinhard Zumkeller, Nov 19 2002

nonn

a(A078129(n))=0; a(A078130(n))=1; a(A078131(n))>0;

Conjecture (lower bound): for all k exists b(k) such that a(n)>k for n>b(k); see b(0)=A078129(83)=154 and b(1)=A078130(63)=218.

			a(160)=4: 160 = 20*2^3 = 4^3+12*2^3 = 2*4^3+4*2^3 = 5^3+3^3+2^3.

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of cubes
Eric Weisstein's World of Mathematics, Cubic Number.

Cf. A000578, A003108, A001235, A078132, A078133, A078134.

nmax = 105; CoefficientList[Series[Product[1/(1 - x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x] // Differences (* Jean-François Alcover, Mar 01 2019, after Vaclav Kotesovec *)

a(n) = 1/n*Sum_{k=1..n} (b(k)-1)*a(n-k), a(0) = 1, where b(k) is sum of cube divisors of k. - Vladeta Jovovic, Nov 20 2002
From Vaclav Kotesovec, Jan 05 2017: (Start)
a(n) = A003108(n) - A003108(n-1).
a(n) ~ exp(4*(Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4) / 3^(3/2)) * (Gamma(1/3) * Zeta(4/3))^(3/2) / (8 * 3^(5/2) * Pi^2 * n^2).
(End)

A078133 Primes which cannot be written as sum of cubes>1.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 61, 71, 73, 79, 101, 103, 109, 127

Offset: 1

Reinhard Zumkeller, Nov 19 2002

Sequence is finite, see A078129.

Eric Weisstein's World of Mathematics, Cubic Number.
Index entries for sequences related to sums of cubes

Cf. A000578, A078128, A078132, A000040, A078139.

A078138 Primes which can be written as sum of squares > 1.

Original entry on oeis.org

13, 17, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

Reinhard Zumkeller, Nov 19 2002

By Sylvester's solution to the Frobenius problem, all integers greater than 4*9 - 4 - 9 = 23 can be represented as a sum of multiples of 4 and 9. Hence all primes except 2,3,5,7,11,19,23 are in this sequence. [Charles R Greathouse IV, Apr 19 2010]

			A000040(11) = 31 = 3^2 + 3^2 + 3^2 + 2^2, therefore 31 is a term.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
J. J. Sylvester, "Question 7382" in Mathematical Questions from the Educational Times, 37 (1884), p. 26 (search for 7382).
Eric Weisstein's World of Mathematics, Sum of Squares Function
Eric Weisstein's World of Mathematics, Coin Problem
Index entries for sequences related to sums of squares

Cf. A078134, A078139, A078132.

Join[{13,17},Prime[Range[10,100]]] (* Harvey P. Dale, May 12 2014 *)

PARI
```
a(n)=if(n<3,[13,17][n],prime(n+7))
```

Comments, reference, and links by Charles R Greathouse IV, Apr 19 2010

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A078128 Number of ways to write n as sum of cubes > 1.

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A078133 Primes which cannot be written as sum of cubes>1.

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A078138 Primes which can be written as sum of squares > 1.

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