A154367 Numbers k such that the sum of the prime factors of composite(k) (with multiplicity) is prime and lpf(composite(k)) + gpf(composite(k)) is composite.

18, 30, 36, 39, 44, 53, 54, 73, 76, 86, 112, 113, 116, 126, 132, 134, 141, 160, 163, 175, 191, 194, 197, 211, 214, 219, 231, 233, 250, 258, 265, 276, 279, 294, 295, 301, 308, 311, 312, 320, 325, 331, 333, 335, 338, 340, 341, 350, 351, 361, 376, 383, 385, 394

Offset: 1

Author

Juri-Stepan Gerasimov, Jan 08 2009

Keywords

• nonn

Examples

			18 is a term because composite(18) = 28 = 2*2*7, 2 + 2 + 7 = 11 is prime, and 2 + 7 = 9 is composite.
30 is a term because composite(30) = 45 = 3*3*5, 3 + 3 + 5 = 11 is prime, and 3 + 5 = 8 is composite.
		

Crossrefs

Cf. A000040 (primes), A002808 (composites).

Programs

Maple

isA002808 := proc(n) n >= 4 and not isprime(n) ; end proc:
A046343 := proc(n) pss(A002808(n)) ; end proc:
A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:
A006530 := proc(n) numtheory[factorset](n) ; max(op(%)) ; end proc:
for n from 1 to 500 do if isprime(A046343(n)) and isA002808( A020639(A002808(n)) + A006530(A002808(n)) ) then printf("%d,",n) ; end if; end do: # R. J. Mathar, May 05 2010

Extensions

Corrected (44 inserted, 120 removed, 146 removed) and extended by R. J. Mathar, May 05 2010

Name and Example section edited by Jon E. Schoenfield, Feb 11 2019