This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A134613 #21 Jun 13 2022 07:47:56 %S A134613 1,1512,337365,375360,523809,1177176,1255254,1380918,1549431,2277345, %T A134613 2286144,2816883,3320713,3340428,3838185,4378333,6726969,7043655, %U A134613 8311212,10281284,10323390,10666227,10708544,12333468,14185724,15883803,21432000,25760763,27111825 %N A134613 Numbers such that the root mean cube of their prime factors is a nonprime integer (where the root mean cube of c and d is ((c^3+d^3)/2)^(1/3)). %C A134613 The prime factors are taken with multiplicity. %C A134613 Numbers included in A134611, but not in A134612. %C A134613 For n > 1, also numbers included in A134614, but not in A134615; a(2) = 1512 is the minimal number with this property. %C A134613 No prime number and no power (> 1) of a prime number can be a term. %H A134613 Hieronymus Fischer, <a href="/A134613/b134613.txt">Table of n, a(n) for n = 1..411</a> %e A134613 a(1) = 1, since 1 has no prime factors, and so the cube mean is zero (by definition of empty sums). %e A134613 a(2) = 1512, since 1512 = 2*2*2*3*3*3*7 and ((3*2^3+3*3^3+7^3)/7)^(1/3) = 64^(1/3) = 4. %o A134613 (PARI) isok(n) = if (n==1, return(1)); sc = 0; nb = 0; f = factor(n); for (i=1, #f~, sc += f[i, 2]*f[i, 1]^3; nb += f[i, 2]; ); return (type(quot = sc/nb) == "t_INT" && ispower(quot, 3, &cr) && (! isprime(cr))); \\ _Michel Marcus_, Jul 15 2013; corrected Jun 13 2022 %Y A134613 Cf. A001597, A025475, A134333, A134344, A134376. %Y A134613 Cf. A134600, A134602, A134605, A134608, A134617, A134619, A134621. %K A134613 nonn %O A134613 1,2 %A A134613 _Hieronymus Fischer_, Nov 11 2007 %E A134613 Extended, edited and added initial term a(1) = 1 by _Hieronymus Fischer_, May 30 2013