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 A050705 Composite number such that when sum of its prime factors is added or subtracted becomes prime. 10
 10, 12, 14, 15, 20, 21, 26, 33, 35, 38, 44, 48, 51, 65, 68, 86, 93, 96, 111, 112, 116, 123, 161, 188, 201, 203, 206, 209, 210, 215, 221, 278, 297, 300, 304, 306, 321, 352, 356, 371, 384, 395, 398, 413, 420, 441, 471, 485, 524, 533, 543, 545, 546, 551, 570, 626 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime factors counted with multiplicity, e.g., 44 = 2*2*11 so the sum of its prime factors is 15 (not 13). - Harvey P. Dale, May 30 2012 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE E.g., 545 = 5*109 so 545 +- (5+109) = 545 +- 114 = 659 and 431 and both are primes. MATHEMATICA spfQ[n_]:=Module[{s=Total[Times@@@FactorInteger[n]]}, !PrimeQ[n] && PrimeQ[ n+s]&&PrimeQ[n-s]]; Select[Range[700], spfQ] (* Harvey P. Dale, May 30 2012 *) PROG (PARI) lista(nn) = {forcomposite(n=2, nn, f = factor(n); sopfr = sum(j=1, #f~, f[j, 1]*f[j, 2]); if (isprime(n+sopfr) && isprime(n-sopfr), print1(n, ", ")); ); } \\ Michel Marcus, Jul 03 2017 CROSSREFS Cf. A050703, A050704, A050706, A050707, A050708, A050709, A050710. Sequence in context: A116023 A062408 A127653 * A095406 A337028 A050769 Adjacent sequences:  A050702 A050703 A050704 * A050706 A050707 A050708 KEYWORD nonn,nice AUTHOR Patrick De Geest, Aug 15 1999 STATUS approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)