A134612 - OEIS

%I #15 Nov 04 2013 21:50:10

%S 4,8,9,16,25,27,32,49,64,81,121,125,128,169,243,256,289,343,361,512,

%T 529,625,729,841,961,1024,1331,1369,1681,1849,2048,2187,2197,2209,

%U 2401,2809,3125,3481,3721,4096,4489,4913,5041,5329,6241,6561,6859,6889,7921

%N Nonprime numbers such that the root mean cube of their prime factors is a prime (where the root mean cube of c and d is ((c^3+d^3)/2)^(1/3)).

%C The prime factors are taken with multiplicity.

%C All perfect prime powers (A025475) with power > 1 are included. First term not included in A025475 is a(211) = 707265 = A134614(5) = A134615(1).

%C Originally, the first term was 1. This was wrong, since the cube mean of the prime factors of 1 is zero, by definition of the empty sum.

%H Hieronymus Fischer, <a href="/A134612/b134612.txt">Table of n, a(n) for n = 1..8600</a>

%e a(5) = 25, since 25 = 5*5 and ((5^3+5^3)/2)^(1/3) = 5.

%o (PARI) lista(m) = {for (i=2, m, if (! isprime(i), f = factor(i); s = sum (j=1, length(f~), f[j,1]^3*f[j,2]); s /= bigomega(i); if (type(s) == "t_INT" && ispower(s, 3, &p) && isprime(p), print1(i, ", "));););}  \\ _Michel Marcus_, Apr 14 2013

%Y Cf. A001597, A025475, A134333, A134344, A134376.

%Y Cf. A134600, A134602, A134605, A134614, A134617, A134619, A134621.

%K nonn

%O 1,1

%A _Hieronymus Fischer_, Nov 11 2007

%E Edited by _Hieronymus Fischer_, May 30 2013