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 A256150 Oblong numbers n such that sigma(n) is a triangular number. 3
 2, 12, 56, 342, 992, 16256, 17822, 169332, 628056, 1189190, 2720850, 11085570, 35599122, 67100672, 1147210770, 1317435912, 1707135806, 7800334080, 11208986256, 13366943840, 17109032402, 17179738112, 46343540900, 58413331032, 83717924940, 204574837700, 274877382656, 445968192672, 589130699852 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. This sequence is the intersection of A002378 and A045746. LINKS EXAMPLE 2 is in the sequence because 2=1*2 is oblong, and sigma(2)= 1+2=3=2*3/2 is triangular. MATHEMATICA Select[2 Accumulate[Range@10000], MemberQ[Accumulate[Range@10000], DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 17 2015 *) PROG (PARI) {for (i=1, i=10^6, n=i*(i+1); if(ispolygonal(sigma(n), 3), print(n)))} CROSSREFS Cf. A000217, A002378, A139256, A045746, A256149, A256151, A256152. Sequence in context: A296944 A105487 A098453 * A180073 A067125 A177782 Adjacent sequences:  A256147 A256148 A256149 * A256151 A256152 A256153 KEYWORD nonn AUTHOR Antonio Roldán, Mar 16 2015 STATUS approved

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Last modified December 13 09:58 EST 2019. Contains 329968 sequences. (Running on oeis4.)