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

1,1

Links

Table of n, a(n) for n=1..54.

Example

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.

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

Crossrefs

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

Sequence in context: A366964 A032612 A151700 * A161164 A092357 A141115

Adjacent sequences: A154364 A154365 A154366 * A154368 A154369 A154370

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 08 2009

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

Status

approved