A134614 Numbers (excluding primes and powers of primes) such that the root mean cube of their prime factors is an integer (where the root mean cube of c and d is ((c^3+d^3)/2)^(1/3)).

1512, 337365, 375360, 523809, 707265, 1177176, 1255254, 1380918, 1549431, 1922816, 2277345, 2284389, 2286144, 2816883, 3320713, 3340428, 3838185, 4378333, 6726969, 7043655, 8311212, 10281284, 10323390, 10666227, 10708544

Offset

1,1

Comments

The prime factors are taken with multiplicity.

Numbers included in A134611, but not in A025475.

a(1) = 1512 is the minimal number with this property.

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..520

Example

a(1) = 1512, since 1512 = 2*2*2*3*3*3*7 and ((2^3+2^3+2^3+3^3+3^3+3^3+7^3)/7)^(1/3) = 64^(1/3) = 4.

Crossrefs

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

Cf. A134600, A134602, A134605, A134608, A134611, A134619, A134621.

Sequence in context: A276291 A034601 A022059 * A134613 A187294 A107523

Adjacent sequences: A134611 A134612 A134613 * A134615 A134616 A134617

Keyword

nonn

Author

Hieronymus Fischer, Nov 11 2007

Extensions

Minor edits and more terms added by Hieronymus Fischer, May 06 2013, May 30 2013

Status

approved