A134605 Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.

16, 48, 81, 320, 351, 486, 512, 625, 1080, 1260, 1350, 1375, 1792, 1836, 2070, 2145, 2175, 2401, 2730, 2772, 3072, 3150, 3510, 4104, 4305, 4625, 4650, 4655, 4998, 5880, 6000, 6174, 6545, 7098, 7128, 7182, 7650, 7791, 7889, 7956, 9030, 9108, 9295, 9324

Offset

1,1

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Example

a(2)=48 since 48=2*2*2*2*3 and sqrt(4*2^2+3^2)=sqrt(25)=5.

Mathematica

srssQ[n_]:=IntegerQ[Sqrt[Total[Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[ n]]^2]]]; Select[Range[10000], CompositeQ[#]&&srssQ[#]&] (* Harvey P. Dale, Jan 22 2019 *)

Prog

(PARI) is(n)=my(f=factor(n)); issquare(sum(i=1, #f~, f[i, 1]^2*f[i, 2])) && !isprime(n) && n>1 \\ Charles R Greathouse IV, Apr 29 2015

Crossrefs

Cf. A001597, A025475, A134333, A134344, A134376, A134600, A134602, A134608, A134611, A134616, A134618, A134620.

Sequence in context: A069084 A084112 A050428 * A035008 A189972 A023648

Adjacent sequences: A134602 A134603 A134604 * A134606 A134607 A134608

Keyword

nonn

Author

Hieronymus Fischer, Nov 11 2007

Status

approved