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A134605
Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.
20
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
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
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Nov 11 2007
STATUS
approved