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 A213016 Numbers n such that the sum of prime factors of n (counted with multiplicity) is 3 times a prime. 2
 8, 9, 14, 20, 24, 26, 27, 38, 44, 62, 68, 74, 105, 112, 116, 125, 126, 134, 150, 160, 180, 188, 192, 195, 208, 212, 216, 218, 231, 234, 243, 254, 275, 278, 314, 330, 332, 343, 352, 356, 362, 396, 398, 422, 428, 465, 483, 490, 496, 548, 558, 575, 588, 609, 614 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The numbers A100118(n)^3 are in the sequence. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 FORMULA sopfr(n) = 3*p, p prime. EXAMPLE 44 is in the sequence because 44 = 2^2 * 11 => sum of prime factors = 2*2+11 = 15 = 3*5 where 5 is prime. MAPLE with(numtheory):A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end: for m from 1 to 3000 do: if type(A(m)/3, prime)= true then printf(`%d, `, m):else fi:od: MATHEMATICA L = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[PrimeQ[w/3], AppendTo[L, k]], {k, 2, 1000}]; L Select[Range[700], PrimeQ[Total[Times@@@FactorInteger[#]]/3]&] (* Harvey P. Dale, Nov 23 2022 *) CROSSREFS Cf. A001414, A100118, A213015. Sequence in context: A175859 A059869 A327863 * A105833 A323249 A257037 Adjacent sequences: A213013 A213014 A213015 * A213017 A213018 A213019 KEYWORD nonn AUTHOR Michel Lagneau, Jun 02 2012 STATUS approved

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Last modified November 30 04:53 EST 2023. Contains 367453 sequences. (Running on oeis4.)