

A134615


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)).


3



707265, 1922816, 2284389, 12023505, 14689836, 21150800, 29444140, 30682000, 36533504, 39372480, 46309837, 52163097, 67303740, 73558065, 85751055, 107366283, 115291904, 161976045, 190384425, 204399585, 218317275, 231443940, 274960400, 286618640
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The prime factors are taken with multiplicity.
a(1) = 707265 is the minimal number with this property. a(3) = 2284389 is the greatest such number < 10^7.


LINKS



EXAMPLE

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.


PROG

(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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



