cp's OEIS Frontend

A247222 Numbers n such that n = gcd(n^2, sigma(n^2)).

%I A247222 #23 Jun 10 2016 05:08:37
%S A247222 1,39,793,7137,76921,863577,2076867,4317885,8329831,23402223,53695813,
%T A247222 55871145,224905437,243762649,1449786951,2631094837,2781581517,
%U A247222 3606816823,6105766123,6605555983,6838433189,8771312043,13907907585,35225161895,42580779709,56541691089
%N A247222 Numbers n such that n = gcd(n^2, sigma(n^2)).
%C A247222 Previous name was: Numbers n such that numerator(sigma(n^2)/n^2)*denominator(sigma(n^2)/n^2) = sigma(n^2).
%C A247222 That is, numbers n, such that A249670(n^2) = A000203(n^2).
%C A247222 Appears to be a subsequence of A232354.
%H A247222 Giovanni Resta, <a href="/A247222/b247222.txt">Table of n, a(n) for n = 1..48</a> (terms < 10^12)
%e A247222 sigma(39^2)/39^2 = 61/39 = 2379 = sigma(39^2), so 39 is a term.
%t A247222 Select[Range[10^6], GCD[#^2, DivisorSigma[1, #^2]] == # &] (* _Giovanni Resta_, Jun 10 2016 *)
%o A247222 (PARI) isok(n) = {ab = sigma(n^2)/n^2; numerator(ab)*denominator(ab) == sigma(n^2);}
%o A247222 (PARI) {isa(n) = if( n<1, 0, n == gcd(n^2, sigma(n^2)))}; /* _Michael Somos_, Nov 26 2014 */
%Y A247222 Cf. A000203, A249670, A249671.
%K A247222 nonn
%O A247222 1,2
%A A247222 _Michel Marcus_, Nov 26 2014
%E A247222 New name after _Michael Somos_ by _Michel Marcus_, Nov 27 2014
%E A247222 a(13)-a(14) from _Michel Marcus_, Nov 27 2014
%E A247222 a(15)-a(26) from _Giovanni Resta_, Jun 10 2016