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%I #10 Mar 22 2015 10:27:10
%S 2,12,56,342,992,16256,17822,169332,628056,1189190,2720850,11085570,
%T 35599122,67100672,1147210770,1317435912,1707135806,7800334080,
%U 11208986256,13366943840,17109032402,17179738112,46343540900,58413331032,83717924940,204574837700,274877382656,445968192672,589130699852
%N Oblong numbers n such that sigma(n) is a triangular number.
%C The numbers 12, 56, 992, 16256, 67100672,…( A139256(n)), twice even perfect numbers, are in the sequence because are oblong (A139256(n)=2^k*(2^k-1) with 2^k-1 Mersenne prime) and sigma(A139256(n))=sigma(2^k*(2^k-1))=sigma(2^k )*sigma( (2^k-1)=(2^(k+1)-1)*2^(k+1)/2, triangular number.
%C This sequence is the intersection of A002378 and A045746.
%e 2 is in the sequence because 2=1*2 is oblong, and sigma(2)= 1+2=3=2*3/2 is triangular.
%t Select[2 Accumulate[Range@10000], MemberQ[Accumulate[Range@10000], DivisorSigma[1, #]] &] (* _Michael De Vlieger_, Mar 17 2015 *)
%o (PARI) {for (i=1,i=10^6,n=i*(i+1);if(ispolygonal(sigma(n), 3),print(n)))}
%Y Cf. A000217, A002378, A139256, A045746, A256149, A256151, A256152.
%K nonn
%O 1,1
%A _Antonio Roldán_, Mar 16 2015
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