A050705 Composite number such that when the sum of its prime factors is added or subtracted it results in a 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

Extensions

Definition rewritten by Harvey P. Dale, Jan 26 2026

Status

approved