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A256150
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Oblong numbers n such that sigma(n) is a triangular number.
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3
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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2 is in the sequence because 2=1*2 is oblong, and sigma(2)= 1+2=3=2*3/2 is triangular.
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MATHEMATICA
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Select[2 Accumulate[Range@10000], MemberQ[Accumulate[Range@10000], DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 17 2015 *)
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PROG
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(PARI) {for (i=1, i=10^6, n=i*(i+1); if(ispolygonal(sigma(n), 3), print(n)))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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