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

1,1

Links

Charles R Greathouse IV and Zak Seidov, Table of n, a(n) for n = 1..500 (1..100 from Levin)

Example

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.

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:

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 *)

Prog

(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

Crossrefs

Cf. A002522, A180278.

Sequence in context: A205078 A198023 A202761 * A219772 A219290 A156238

Adjacent sequences: A196216 A196217 A196218 * A196220 A196221 A196222

Keyword

nonn

Author

Michel Lagneau, Sep 29 2011

Status

approved