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)).

707265, 1922816, 2284389, 12023505, 14689836, 21150800, 29444140, 30682000, 36533504, 39372480, 46309837, 52163097, 67303740, 73558065, 85751055, 107366283, 115291904, 161976045, 190384425, 204399585, 218317275, 231443940, 274960400, 286618640

Offset

1,1

Comments

The prime factors are taken with multiplicity.

Numbers included in A134612, but not in A025475.

a(1) = 707265 is the minimal number with this property. a(3) = 2284389 is the greatest such number < 10^7.

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..108

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

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

Cf. A134600, A134602, A134605, A134608, A134613, A134617, A134619, A134621.

Sequence in context: A203834 A234701 A140943 * A186607 A249195 A236277

Adjacent sequences: A134612 A134613 A134614 * A134616 A134617 A134618

Keyword

nonn

Author

Hieronymus Fischer, Nov 11 2007

Extensions

More terms and minor edits by Hieronymus Fischer, May 06 2013, May 30 2013

Status

approved