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

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

1,1

Comments

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

Links

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

Example

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

Mathematica

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 *)

Crossrefs

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

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

Sequence in context: A211743 A211752 A211763 * A192215 A347613 A280022

Adjacent sequences: A134604 A134605 A134606 * A134608 A134609 A134610

Keyword

nonn

Author

Hieronymus Fischer, Nov 11 2007

Extensions

Minor edits by Hieronymus Fischer, Apr 19 2013

Status

approved