cp's OEIS Frontend

A232355 Numbers k such that sigma(triangular(k)) = sigma(k)^2.

%I A232355 #28 Nov 04 2024 02:42:06
%S A232355 1,11,695,991,2839,3707,9347,10703,12847,27089,42251,56419,74671,
%T A232355 115289,168739,191051,219295,233729,280111,300731,326899,353651,
%U A232355 430859,611799,642991,661715,1035827,1116607,1181579,1234519,1365491,1485035,1777099,1854671,1905875
%N A232355 Numbers k such that sigma(triangular(k)) = sigma(k)^2.
%C A232355 Subsequence of A116990. - _Michel Marcus_, Jun 13 2015
%H A232355 Amiram Eldar, <a href="/A232355/b232355.txt">Table of n, a(n) for n = 1..100</a>
%e A232355 11 is in the sequence because sigma(11*12/2) = sigma(66) = 144 = 12^2 = sigma(11)^2.
%t A232355 Select[Range@1000000, DivisorSigma[1, #]^2==DivisorSigma[1, (# (# + 1)/2)] &] (* _Vincenzo Librandi_, Jun 13 2015 *)
%o A232355 (PARI) isok(n) = sigma(n)^2 == sigma(n*(n+1)/2); \\ _Michel Marcus_, Nov 23 2013
%o A232355 (Magma) [n: n in [1..7*10^5] | SumOfDivisors(n*(n+1) div 2) eq SumOfDivisors(n)^2]; // _Vincenzo Librandi_, Jun 13 2015
%Y A232355 Cf. A000203 (sigma(n): sum of divisors of n), A000217 (triangular(n): = n*(n+1)/2).
%Y A232355 Cf. A074285 (sigma(triangular(n))), A072861 (sigma(n)^2).
%Y A232355 Cf. A116990 (indices of triangular numbers whose sum of divisors is square).
%K A232355 nonn
%O A232355 1,2
%A A232355 _Alex Ratushnyak_, Nov 22 2013
%E A232355 More terms from _Michel Marcus_, Nov 23 2013