A091350 First occurrence (*2) of n in A088627 - or - least number that yields n different primes if you factorize it in all possible ways in two factors and add these factors.

8, 2, 6, 90, 30, 390, 690, 420, 210, 4290, 3990, 8778, 2310, 3570, 4830, 11550, 38850, 84630, 66990, 79170, 39270, 30030, 51870, 46410, 43890, 111930, 163020, 221340, 419430, 131670, 1902810, 1385670, 1009470, 1452990, 746130, 903210, 570570, 1067430, 1531530

Offset: 0

Author

Matthias Engelhardt, Jan 05 2004

Keywords

• nonn

Comments

a(0) .. a(29) are in the list; additional know values are a(34) = 746130, a(35) = 903210, a(36) = 570570, a(40) = 510510, a(41) = 690690 and a(46) = 870870. If n in { 30, 31, 32, 33, 37, 38, 39, 42, 43, 44, 45}, or if n > 46, then a(n) > 10^6.

a(258) > 10^11. - Donovan Johnson, Oct 15 2013

Examples

			Sequence A088627 starts with 1,1,2,0, meaning that 2 and 4 yield 1 prime, 6 yields 2 and 8 yields 0 primes; therefore a(0) = 8, a(1) = 2 and a(2) = 6.
		

Links

• T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 0..257 (terms up to a(90) from T. D. Noe)
• M. Engelhardt, Number of Primes arising as Sum of a Factorization.

Crossrefs

Cf. A088627.

Programs

Java

// Programs available from Matthias Engelhardt.

Mathematica

DivPrimes[n_Integer] := Length[Select[Union[Divisors[n]+Reverse[Divisors[n]]], PrimeQ]]; nn=40; t=Table[0,{nn}]; cnt=0; k=0; While[cntT. D. Noe, Aug 02 2010 *)

Extensions

Extended by T. D. Noe, Aug 02 2010