A196219 Numbers n such that n^2 is divisible by the sum of the distinct prime divisors of n^2 + 1.
7, 18, 187, 378, 1560, 1683, 1710, 1719, 4697, 7788, 8832, 10693, 21708, 22968, 27378, 28322, 29032, 30016, 30635, 32220, 32368, 33813, 36725, 41028, 42444, 44733, 45630, 45985, 50085, 57768, 69936, 81639, 86420, 87116, 92667, 95418, 96348, 97185, 114100
Offset: 1
Keywords
Examples
1560 is in the sequence because the sum of the prime distinct divisors of 1560^2+1 is 17+37+53+73=180 and 1560^2 /180=13520.
Links
- Charles R Greathouse IV and Zak Seidov, Table of n, a(n) for n = 1..500 (1..100 from Levin)
Programs
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Maple
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):else fi:od:
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Mathematica
c=0;s={};Do[If[PowerMod[n,2,Plus@@First/@FactorInteger[n^2+1]]==0,AppendTo[s,n];c++;If[c==100,Break[]]],{n,2*10^6}];s (* Zak Seidov, Oct 14 2011 *) -
PARI
is(n)=my(f=factor(n^2+1)[,1]);n^2%sum(i=1,#f,f[i])==0 \\ Charles R Greathouse IV, Oct 25 2011