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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.
0
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
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
KEYWORD
nonn
AUTHOR
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