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%I #15 Aug 19 2019 03:17:06
%S 1,36,441,5625,6084,407044,8444836,17388900,35070084,40729924,
%T 57790404,80138304,537822481,588159504,659821969,918999225,1820387556,
%U 2179862721,2599062361,5110963081,28816420516,36144473689,46082779561,55145598561,147225690000,163405126756
%N Square numbers n such that sigma(n) is a triangular number.
%C This sequence is the intersection of A000290 and A045746.
%H Amiram Eldar, <a href="/A256149/b256149.txt">Table of n, a(n) for n = 1..72</a>
%e 441 is in the sequence because 441 = 21^2 is square number, and sigma(441) = 441 + 147 + 63 + 49 + 21 + 9 + 7 + 3 + 1 = 741 = 38*39/2 is triangular number.
%t t = Accumulate[Range@ 10000]; Select[Range[10000]^2, MemberQ[t, DivisorSigma[1, #]] &] (* _Michael De Vlieger_, Mar 17 2015 *)
%t Select[Range[500000]^2,OddQ[Sqrt[8DivisorSigma[1,#]+1]]&] (* _Harvey P. Dale_, Feb 25 2017 *)
%o (PARI) {for(i=1,10^6,n=i*i;if(ispolygonal(sigma(n), 3),print1(n,", ")))}
%Y Cf. A000290, A000217, A045746, A083674, A256150, A256151, A256152.
%K nonn
%O 1,2
%A _Antonio Roldán_, Mar 16 2015
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