A134611 -id:A134611 - cp's OEIS frontend

A134609 Numbers such that the cube root of the sum of cubes of their prime factors is a nonprime integer.

256, 588, 693, 3840, 6561, 17787, 178360, 313600, 337365, 350000, 387072, 390625, 407442, 432000, 531674, 535815, 541310, 664909, 697851, 1044582, 1262056, 1264640, 1299272, 1374327, 1547570, 1660360, 1740024, 2160756, 2578968

Offset: 1

Hieronymus Fischer, Nov 11 2007

nonn

No prime number is a term. Hieronymus Fischer, Apr 20 2013

			a(2)=588, since 588=2*2*3*7*7 and (2*2^3+3^3+2*7^3)^(1/3)=729^(1/3)=81.

Hieronymus Fischer, Table of n, a(n) for n = 1..250

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

Cf. A134600, A134602, A134605, A134611, A134616, A134618, A134620.

Minor Edits by Hieronymus Fischer, Apr 20 2013

A134607 Composite numbers such that the square root of the sum of squares of their prime factors is a prime.

Original entry on oeis.org

48, 320, 486, 3072, 3150, 6174, 7128, 7650, 10890, 11466, 15000, 18018, 18810, 25578, 27846, 29400, 30240, 39546, 40590, 45056, 45927, 53010, 54600, 55062, 59202, 73440, 75582, 77418, 80910, 85800, 90552, 92106, 95238, 96642, 98838

Offset: 1

Hieronymus Fischer, Nov 11 2007

nonn

Numbers included in A134605, but not in A134606. a(1)=48 is the minimal number with this property.

			a(2)=320, since 320=2*2*2*2*2*2*5 and sqrt(6*2^2+5^2)=sqrt(49)=7.

Hieronymus Fischer, Table of n, a(n) for n = 1..1000

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

Cf. A134600, A134602, A134605, A134611, A134616, A134618, A134620.

sspfpQ[n_]:=PrimeQ[Sqrt[Total[Flatten[Table[#[[1]],{#[[2]]}]&/@ FactorInteger[ n]]^2]]]; upto=100000;With[{comps=Complement[ Range[ upto],Prime[ Range[PrimePi[upto]]]]},Select[comps,sspfpQ]] (* Harvey P. Dale, Jul 10 2013 *)

Minor edits by Hieronymus Fischer, Apr 19 2013

cp's OEIS Frontend

A134609 Numbers such that the cube root of the sum of cubes of their prime factors is a nonprime integer.

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