A163517 If m-th composite is the product of k1-th prime, k2-th prime,..,kr-th prime and prime=k1+k2+..+kr then set a(n)=m.

1, 2, 3, 7, 8, 10, 11, 14, 16, 20, 21, 23, 28, 29, 30, 34, 37, 39, 41, 42, 49, 51, 52, 57, 67, 68, 70, 71, 78, 83, 88, 91, 93, 96, 106, 108, 110, 115, 116, 120, 123, 130, 133, 136, 139, 145, 150, 157, 160, 162, 166, 167, 171, 173, 177, 179, 180, 181, 182, 184, 188, 191

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 30 2009

Keywords

• nonn

Examples

			1st composite=4=2*2=prime(1)*prime(1) and 1+1=2 prime, so a(1)=1.
2nd composite=6=2*3=prime(1)*prime(2) and 1+2=3 prime, so a(2)=2.
3rd composite=8=2*2*2=prime(1)*prime(1)*prime(1) and 1+1+1=3 prime, so a(3)=3.
7th composite=14=2*7=prime(1)*prime(4) and 1+4=5 prime, so a(4)=7.
		

Crossrefs

Cf. A000040, A002808, A061395.

Programs

Maple

A056239 := proc(n) pfs := ifactors(n)[2] ; add ( op(2,d)*numtheory[pi](op(1,d)), d=pfs) ; end: A002808 := proc(n) option remember ; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: for n from 1 to 300 do if isprime(A056239( A002808(n))) then printf("%d,",n) ; fi; od: # R. J. Mathar, Aug 01 2009

Extensions

Values from a(16) on corrected by R. J. Mathar, Aug 01 2009