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A342957 a(n) is the least k such that A342956(k) = n.

%I A342957 #17 Aug 20 2021 16:01:24
%S A342957 1,2,4,15,39,87,183,951,1255,1527,3063,15335,12279,61431,49143,516047,
%T A342957 491495,1703767,1310695,8257487,3145719,15728631,12582903,94371815,
%U A342957 50331639,352321527,335544295
%N A342957 a(n) is the least k such that A342956(k) = n.
%C A342957 a(n) exists for all n, as A342956(2^(2^k)) = k+1.
%C A342957 If 2^n = p+q where p and q are primes, then A342956(p*q) = n so a(n) <= p*q <= 2^(2*n-2).  Goldbach's conjecture implies such p and q exist for all n >= 2.
%e A342957 a(3) = 15 because A342956(15) = 3 and this is the first appearance of the value 3 in A342956.
%p A342957 f:= proc(n) local t; numtheory:-bigomega(add(t[1]*t[2], t=ifactors(n)[2])) end proc:
%p A342957 V:= Array(0..18): count:= 0:
%p A342957 for n from 0 while count < 19 do
%p A342957 v:= f(n):
%p A342957 if v <= 19 and V[v] = 0 then
%p A342957     count:= count+1; V[v]:= n
%p A342957 fi
%p A342957 od:
%p A342957 convert(V,list);
%t A342957 Table[n=0;While[PrimeOmega[Plus@@Times@@@FactorInteger@++n]!=k];n,{k,0,14}] (* _Giorgos Kalogeropoulos_, Aug 20 2021 *)
%Y A342957 Cf. A342956.
%K A342957 nonn,more
%O A342957 0,2
%A A342957 _J. M. Bergot_ and _Robert Israel_, Mar 30 2021
%E A342957 a(25)-a(26) from _Chai Wah Wu_, Mar 31 2021