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

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn
• nice

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

Examples

			E.g., 545 = 5*109 so 545 +- (5+109) = 545 +- 114 = 659 and 431 and both are primes.
		

Links

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

Crossrefs

Cf. A050703, A050704, A050706, A050707, A050708, A050709, A050710.

Programs

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 *)

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