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 A046363 Composite numbers whose sum of prime factors (with multiplicity) is prime. 20
 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 Conjecture: a(n) can be approximated with the formula c*n^k, where c is approximately 0.46 and k is approximately 1.05. - Elijah Beregovsky, May 01 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 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): map(proc (x) options operator, arrow: seq(x, j = 1 .. x) 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}] & /@ FactorInteger[n]]; GenerateA046363[n_] := Select[Range[n], PrimeQ[PrimeFactorsAdded[ # ]] && PrimeQ[ # ] == False &]; (* GenerateA046363 would give all elements of this sequence below 100. - Ryan Witko (witko(AT)nyu.edu), Mar 08 2004 *) Select[Range, !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 October 23 14:54 EDT 2019. Contains 328345 sequences. (Running on oeis4.)