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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

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.

EXAMPLE

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.

MATHEMATICA

DivPrimes[n_Integer] := Length[Select[Union[Divisors[n]+Reverse[Divisors[n]]], PrimeQ]]; nn=40; t=Table[0, {nn}]; cnt=0; k=0; While[cnt<nn, k=k+2; m=DivPrimes[k]; If[0<m<=nn && t[[m]]==0, t[[m]]=k; cnt++ ]]; Prepend[t, 8] [From T. D. Noe, Aug 02 2010]

PROG

Java programs available from Matthias Engelhardt.

CROSSREFS

Cf. A088627.

Sequence in context: A240976 A199158 A086089 * A099876 A153203 A261829

Adjacent sequences:  A091347 A091348 A091349 * A091351 A091352 A091353

KEYWORD

nonn

AUTHOR

Matthias Engelhardt, Jan 05 2004

EXTENSIONS

Extended by T. D. Noe, Aug 02 2010

STATUS

approved

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Last modified February 23 08:18 EST 2019. Contains 320420 sequences. (Running on oeis4.)