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

1,2

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A010429 A140282 A161757 * A163408 A060299 A120512

Adjacent sequences: A134373 A134374 A134375 * A134377 A134378 A134379

Keyword

nonn

Author

Hieronymus Fischer, Oct 23 2007

Extensions

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

Status

approved