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Search: id:A128510
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| A128510 |
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Composites c such that c*A001414(c) is adjacent to a prime. |
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1
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| 4, 6, 8, 9, 10, 12, 14, 16, 20, 21, 25, 26, 28, 33, 34, 35, 36, 38, 40, 42, 44, 46, 50, 51, 52, 54, 55, 56, 60, 64, 65, 68, 72, 74, 76, 80, 81, 82, 85, 90, 93, 95, 96, 98, 100, 102, 110, 111, 115, 119, 121, 122, 123, 124, 126, 132, 133, 135, 138, 140, 143, 144, 145, 146, 148, 150
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The composites c of A002808 are multiplied by the sum of their prime factors (with multiplicity),
and are placed into the sequence of that product is in A045718.
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EXAMPLE
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c = 52= A002808(74) has prime factor sum A001414(52) = 17, and 52*17 = 883+1 is one away from the prime 883, which adds 52 to the sequence.
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MAPLE
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A001414 := proc(n) local fcts, d ; fcts := ifactors(n)[2] ; add(op(1, d)*op(2, d), d=fcts) ; end proc:
isA045718 := proc(n) isprime(n+1) or isprime(n-1) ; end proc:
isA128510 := proc(n) local c; if not isprime(n) then c := n*A001414(n) ; isA045718(c) ; else false; end if ; end proc:
for n from 4 to 500 do if isA128510(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Nov 02 2009
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CROSSREFS
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Cf. A066073.
Sequence in context: A090419 A070810 A129930 this_sequence A109289 A066071 A067013
Adjacent sequences: A128507 A128508 A128509 this_sequence A128511 A128512 A128513
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KEYWORD
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nonn,easy,new
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), May 07 2007
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EXTENSIONS
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8 inserted and sequence extended - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2009
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