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A307034 a(n) is the smallest integer k of the form k = x*(x + a(n-1)), such that A324920(k) = n, for some positive integer x, with a(0) = 0.

%I A307034 #16 May 25 2019 16:31:16
%S A307034 0,1,2,3,10,11,26,87,178,179,362,1835,22164,155197,620804,5587317,
%T A307034 55873270,167619819,1340958616,57661222337,345967334058,
%U A307034 25255615391563,858690923314298,4293454616571515,60108364632001406,3185743325496077327,178401626227780333448,1605614636050023001113
%N A307034 a(n) is the smallest integer k of the form k = x*(x + a(n-1)), such that A324920(k) = n, for some positive integer x, with a(0) = 0.
%C A307034 Inspired by A324921.
%C A307034 This sequence provides upper bounds for A324921, i.e.: A324921(n) <= a(n).
%o A307034 (PARI)
%o A307034 f(n) = my(d=divisors(n)); d[(2+#d)\2]-d[(1+#d)\2]; \\ A056737
%o A307034 g(n) = my(k=0); while(n!=0, k++; n=f(n)); k; \\ A324920
%o A307034 a(n) = if(n <= 0, return(0)); my(t=a(n-1)); for(k=1, oo, if(g(k*(k+t)) == n, return(k*(k+t))));
%Y A307034 Cf. A056737, A324920, A324921.
%K A307034 nonn
%O A307034 0,3
%A A307034 _Daniel Suteu_ and _Robert G. Wilson v_, Mar 23 2019