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A046363 Composite numbers whose sum of prime factors (with multiplicity) is prime. 19
6, 10, 12, 22, 28, 34, 40, 45, 48, 52, 54, 56, 58, 63, 75, 76, 80, 82, 88, 90, 96, 99, 104, 108, 117, 118, 136, 142, 147, 148, 153, 165, 172, 175, 176, 184, 198, 202, 207, 210, 214, 224, 245, 248, 250, 252, 268, 273, 274, 279, 294, 296, 298, 300, 316, 320, 325 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If prime numbers were included the sequence would be 2,3,5,6,7,10,11, 12,13,17,19,22,23,28,29,... which is A100118. - Hieronymus Fischer, Oct 20 2007

LINKS

Table of n, a(n) for n=1..57.

FORMULA

A100118 INTERSECT A002808. - R. J. Mathar, Sep 09 2015

EXAMPLE

214 = 2 * 107 -> Sum of factors is 109 -> 109 is prime.

MAPLE

ifac := proc (n) local L, x: L := ifactors(n)[2]: map(proc (x) options operator, arrow: seq(x[1], j = 1 .. x[2]) end proc, L) end proc: a := proc (n) if isprime(n) = false and isprime(add(t, t = ifac(n))) = true then n else end if end proc: seq(a(n), n = 1 .. 350); # with help from W. Edwin Clark - Emeric Deutsch, Jan 21 2009

MATHEMATICA

PrimeFactorsAdded[n_] := Plus @@ Flatten[Table[ #[[1]]*#[[2]], {1}] & /@ FactorInteger[n]]; GenerateA046363[n_] := Select[Range[n], PrimeQ[PrimeFactorsAdded[ # ]] && PrimeQ[ # ] == False &]; (* GenerateA046363[100] would give all elements of this sequence below 100. - Ryan Witko (witko(AT)nyu.edu), Mar 08 2004 *)

Select[Range[325], !PrimeQ[#] && PrimeQ[Total[Times@@@FactorInteger[#]]]&] (* Jayanta Basu, May 29 2013 *)

PROG

(PARI) is(n)=if(isprime(n), return(0)); my(f=factor(n)); isprime(sum(i=1, #f~, f[i, 1]*f[i, 2])) \\ Charles R Greathouse IV, Sep 21 2013

CROSSREFS

Cf. A046364, A046365, A100118, A000040, A002808, A066038, A001414.

Sequence in context: A315137 A315138 A315139 * A101086 A297620 A074924

Adjacent sequences:  A046360 A046361 A046362 * A046364 A046365 A046366

KEYWORD

nonn,changed

AUTHOR

Patrick De Geest, Jun 15 1998

EXTENSIONS

Edited by R. J. Mathar, Nov 02 2009

STATUS

approved

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Last modified December 18 16:37 EST 2018. Contains 318229 sequences. (Running on oeis4.)