A134376 Numbers whose sum of prime factors (counted with multiplicity) is not prime.

1, 4, 8, 9, 14, 15, 16, 18, 20, 21, 24, 25, 26, 27, 30, 32, 33, 35, 36, 38, 39, 42, 44, 46, 49, 50, 51, 55, 57, 60, 62, 64, 65, 66, 68, 69, 70, 72, 74, 77, 78, 81, 84, 85, 86, 87, 91, 92, 93, 94, 95, 98, 100, 102, 105, 106, 110, 111, 112, 114, 115, 116, 119, 120, 121, 122

Offset: 1

Author

Hieronymus Fischer, Oct 23 2007

Keywords

• nonn

Comments

The first term is 1, since 1 has no prime factors and so the sum of prime factors evaluates to zero.

Conjecture: a(n) ~ n. - Charles R Greathouse IV, Apr 28 2015

Examples

			a(2) = 4, since 4 = 2*2 and 2+2 = 4 is not prime.
a(5) = 14, since 14 = 2*7 and 2+7 = 9 is not prime.
		

Links

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

Crossrefs

Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134334, A134344, A078177.

Programs

Mathematica

Select[Range[150],!PrimeQ[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ #]]]]&] (* Harvey P. Dale, Jul 05 2021 *)

PARI

sopfr(n)=my(f=factor(n)); sum(i=1,#f~,f[i,1]*f[i,2])
is(n)=!isprime(sopfr(n)) \\ Charles R Greathouse IV, Apr 28 2015

Extensions

Edited by the author at the suggestion of T. D. Noe, May 20 2013