A047718 - OEIS

%I #16 Jul 22 2021 07:56:30

%S 7,22,37,52,67,87,102,112,117,132,147,167,177,182,197,212,227,242,247,

%T 262,277,292,307,322,327,342,352,357,372,387,402,407,417,422,437,452,

%U 467,482,487,502,517,532,547,562,567,577,582,592,597,612,631,646,662

%N Numbers that are the sum of 7 but no fewer nonzero fourth powers.

%H David A. Corneth, <a href="/A047718/b047718.txt">Table of n, a(n) for n = 1..26439</a> (terms <= 200000)

%o (PARI) upto(n)={my(e=7); my(s=sum(k=1, sqrtint(sqrtint(n)), x^(k^4)) + O(x*x^n)); my(p=s^e, q=(1 + s)^(e-1)); select(k->polcoeff(p,k) && !polcoeff(q,k), [1..n])} \\ _Andrew Howroyd_, Jul 06 2018

%o (Python)

%o from itertools import combinations_with_replacement as mc

%o def aupto(limit):

%o     qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 6 <= limit]

%o     ss = [set(sum(c) for c in mc(qd, i)) for i in range(8)]

%o     s7nf = ss[7] - ss[6] - ss[5] - ss[4] - ss[3] - ss[2] - ss[1]

%o     return sorted(s for s in s7nf if s <= limit)

%o print(aupto(663)) # _Michael S. Branicky_, Jul 22 2021

%Y Cf. A000583, A002377, A003341.

%K nonn

%O 1,1

%A Arlin Anderson (starship1(AT)gmail.com)