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%I #23 Nov 04 2013 21:50:48
%S 707265,1922816,2284389,12023505,14689836,21150800,29444140,30682000,
%T 36533504,39372480,46309837,52163097,67303740,73558065,85751055,
%U 107366283,115291904,161976045,190384425,204399585,218317275,231443940,274960400,286618640
%N Numbers (excluding primes and powers of primes) 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 Numbers included in A134612, but not in A025475.
%C a(1) = 707265 is the minimal number with this property. a(3) = 2284389 is the greatest such number < 10^7.
%H Hieronymus Fischer, <a href="/A134615/b134615.txt">Table of n, a(n) for n = 1..108</a>
%e a(1) = 707265, since 707265 = 3*3*3*5*13*13*31 and ((3*3^3+5^3+2*13^3+31^3)/7)^(1/3) = 4913^(1/3) = 17.
%o (PARI) isok(n) = {if (omega(n) == 1, return (0)); f = factor(n); s = sum(i=1, #f~, f[i,2]*f[i,1]^3); s = s/bigomega(n); if (type(s) != "t_INT", return (0)); if (! ispower(s, 3, &p), return (0)); isprime(p);} \\ _Michel Marcus_, Nov 03 2013
%Y Cf. A001597, A025475, A134333, A134344, A134376.
%Y Cf. A134600, A134602, A134605, A134608, A134613, A134617, A134619, A134621.
%K nonn
%O 1,1
%A _Hieronymus Fischer_, Nov 11 2007
%E More terms and minor edits by _Hieronymus Fischer_, May 06 2013, May 30 2013
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