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%I #14 Mar 09 2020 09:12:00
%S 7,18,121,2268,13520,1377,8550,5157,7381,8496,76176,83521,161604,
%T 284229,1028196,4092529,275804,274432,336985,1153476,962948,48841,
%U 319225,276676,617796,3946827,684450,156349,632025,1256454,6368547,244917,2506180,2256004,5410947
%N Integer quotients of k^2 by the sum of the prime distinct divisors of k^2+1, where k = A196219(n).
%C Generated by k = 7, 18, 187, 378, 1560, 1683, … (A196219).
%H Amiram Eldar, <a href="/A196220/b196220.txt">Table of n, a(n) for n = 1..500</a> (calculated from the b-file at A196219)
%F a(n) = A196219(n)^2/A008472(A196219(n)^2 + 1). - _Amiram Eldar_, Mar 09 2020
%e For k = 378, the prime distinct divisors of 378^2 + 1 are 5, 17, 41 and 378^2 /(5+17+41) = 2268. Hence 2268 is in the sequence.
%p with(numtheory):for k from 1 to 120000 do: y:=factorset(k^2+1): s:=sum(y[i],i=1..nops(y)):if irem(k^2,s)=0 then printf(`%d, `, k^2/s):else fi:od:
%t Select[Table[n^2/Total[Transpose[FactorInteger[n^2+1]][[1]]],{n,10^5}],IntegerQ] (* _Harvey P. Dale_, Apr 18 2015 *)
%Y Cf. A002522, A008472, A180278, A196219.
%K nonn
%O 1,1
%A _Michel Lagneau_, Sep 29 2011