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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.

%I A091350 #26 Aug 10 2025 16:52:29
%S A091350 8,2,6,90,30,390,690,420,210,4290,3990,8778,2310,3570,4830,11550,
%T A091350 38850,84630,66990,79170,39270,30030,51870,46410,43890,111930,163020,
%U A091350 221340,419430,131670,1902810,1385670,1009470,1452990,746130,903210,570570,1067430,1531530
%N 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.
%C A091350 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.
%C A091350 a(258) > 10^11. - _Donovan Johnson_, Oct 15 2013
%H A091350 T. D. Noe and Donovan Johnson, <a href="/A091350/b091350.txt">Table of n, a(n) for n = 0..257</a> (terms up to a(90) from T. D. Noe)
%H A091350 M. Engelhardt, <a href="http://nqueens.de/otherTopics/SumOfFactorPrimes.en.html">Number of Primes arising as Sum of a Factorization</a>.
%e A091350 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.
%t A091350 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] (* _T. D. Noe_, Aug 02 2010 *)
%o A091350 (Java) // Programs available from _Matthias Engelhardt_.
%Y A091350 Cf. A088627.
%K A091350 nonn
%O A091350 0,1
%A A091350 _Matthias Engelhardt_, Jan 05 2004
%E A091350 Extended by _T. D. Noe_, Aug 02 2010