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A088709 Numbers n that are a product of two primes j and k such that n+j+k is prime. 3
6, 10, 14, 15, 21, 26, 33, 34, 35, 38, 46, 51, 55, 57, 58, 65, 74, 85, 86, 93, 111, 118, 123, 141, 143, 145, 155, 158, 161, 166, 177, 178, 185, 194, 201, 203, 205, 206, 209, 215, 221, 254, 267, 278, 295, 298, 319, 321, 323, 326, 327, 329, 334, 341, 346, 355, 365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n > 1, for which sigma(n+n') = sigma(n), where n' is the arithmetic derivative of n. - Paolo P. Lava, Apr 24 2012

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(2)=10 because 10 has only one pair of prime factors (2 and 5) and 10 + 2 + 5 = 17, which is prime.

MATHEMATICA

lst={}; Do[If[FactorInteger[n][[1, 2]]==1&&FactorInteger[n][[2, 2]]==1, If[FactorInteger[n][[1, 1]]*FactorInteger[n][[2, 1]]==n, If[PrimeQ[p=n+FactorInteger[n][[1, 1]]+FactorInteger[n][[2, 1]]], AppendTo[lst, n]]]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 19 2009 *)

ptpQ[n_]:=Module[{fi=FactorInteger[n]}, Length[fi]==2&&Union[ fi[[All, 2]]] == {1}&&PrimeQ[n+Total[fi[[All, 1]]]]]; Select[Range[400], ptpQ] (* Harvey P. Dale, Nov 06 2020 *)

CROSSREFS

Cf. A001358.

Sequence in context: A093772 A046400 A100660 * A225706 A063078 A064452

Adjacent sequences:  A088706 A088707 A088708 * A088710 A088711 A088712

KEYWORD

nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Oct 11 2003

STATUS

approved

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Last modified August 4 15:53 EDT 2021. Contains 346447 sequences. (Running on oeis4.)