A200677 Smallest semiprime such that the sum of the two prime factors equals n, or zero if impossible.

0, 0, 0, 4, 6, 9, 10, 15, 14, 21, 0, 35, 22, 33, 26, 39, 0, 65, 34, 51, 38, 57, 0, 95, 46, 69, 0, 115, 0, 161, 58, 87, 62, 93, 0, 155, 0, 217, 74, 111, 0, 185, 82, 123, 86, 129, 0, 215, 94, 141, 0, 235, 0, 329, 106, 159, 0, 265, 0, 371, 118, 177, 122, 183, 0

Offset: 1

Author

Michel Lagneau, Nov 20 2011

Keywords

• nonn

Comments

For n > 3, a(n) = 0 if n-2 is an odd composite.

The sequence without zeros is a subsequence of A189553. - Manfred Scheucher, Aug 08 2015

The two prime factors are not necessarily distinct; a(6) = 9, both of whose prime factors are 3s. - Jon E. Schoenfield, Aug 09 2015

Examples

			a(10) = 21 because 21 = 3*7 and 3+7 = 10, and there is no semiprime smaller than 21 whose two prime factors sum to 10.
		

Crossrefs

Cf. A001358, A014091, A014092, A135093.

Programs

Maple

with(numtheory):for n from 1 to 65 do:ii:=0:for k from 1 to 1000 while(ii=0)do:m1:=bigomega(k):x:=factorset(k): m2:=nops(x):if m1=2 and m2=2 and x[1]+x[2]= n or m1=2 and m2=1 and 2*x[1]= n then ii:=1: printf(`%d, `,k):else fi:od:if ii=0 then printf(`%d, `,0):else fi:od:

Formula

a(A014091(n)) > 0; a(A014092(n)) = 0. - Michel Marcus, Aug 10 2015

Extensions

Edited by Jon E. Schoenfield and Manfred Scheucher, Aug 09 2015