A128510 Composites c such that c*A001414(c) is adjacent to a prime.

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

Offset

1,1

Comments

The composites c of A002808 are multiplied by the sum of their prime factors (with multiplicity), and are placed into the sequence if that product is in A045718.

Links

Table of n, a(n) for n=1..66.

Example

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.

Maple

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

Crossrefs

Cf. A066073.

Sequence in context: A070810 A227180 A129930 * A109289 A066071 A306307

Adjacent sequences: A128507 A128508 A128509 * A128511 A128512 A128513

Keyword

nonn,easy

Author

J. M. Bergot, May 07 2007

Extensions

8 inserted and sequence extended by R. J. Mathar, Nov 02 2009

Status

approved