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A073939 Least m such that A078142(m) gives the n-th prime, where A078142(n) is the sum of the differences of the distinct prime factors p of n and the next square larger than p.

%I A073939 #10 Dec 08 2019 12:24:20
%S A073939 2,6,11,22,53,106,83,166,173,227,293,863,443,857,853,971,1097,2194,
%T A073939 1229,1373,2746,2837,2221,2027,2819,3499,4253,3257,3491,3251,4229,
%U A073939 4493,5639,6917,6907,7949,6899,7937,7229,7927,11057,10223,9413,10211,9803
%N A073939 Least m such that A078142(m) gives the n-th prime, where A078142(n) is the sum of the differences of the distinct prime factors p of n and the next square larger than p.
%H A073939 Amiram Eldar, <a href="/A073939/b073939.txt">Table of n, a(n) for n = 1..10000</a>
%e A073939 a(4)=22 because A078142(22)=7, the fourth prime and this is the first time 7 occurs.
%t A073939 s[n_] := Total[Ceiling[Sqrt[(p = FactorInteger[n][[;; , 1]])]]^2 - p]; max=45; seq=Table[0,{max}]; c = 0; n=1; While[c<max, s1=s[n]; If[PrimeQ[s1], i=PrimePi[s1]; If[i<=max && seq[[i]]==0, c++; seq[[i]] = n]]; n++]; seq (* _Amiram Eldar_, Dec 08 2019 *)
%Y A073939 Cf. A078142.
%K A073939 nonn
%O A073939 1,1
%A A073939 _Jason Earls_, Nov 20 2002