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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

Table of n, a(n) for n=1..29.

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: A044047 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 July 25 04:48 EDT 2017. Contains 289779 sequences.