A050705 Composite number such that when sum of its prime factors is added or subtracted becomes prime.

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

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