A256150 Oblong numbers n such that sigma(n) is a triangular number.

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

Offset

1,1

Comments

The numbers 12, 56, 992, 16256, 67100672, ... (A139256(n), twice even perfect numbers) are in the sequence because they are oblong (A139256(n) = 2^k*(2^k-1)) 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 is a 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: A296944 A105487 A098453 * A180073 A363402 A067125

Adjacent sequences: A256147 A256148 A256149 * A256151 A256152 A256153

Keyword

nonn

Author

Antonio Roldán, Mar 16 2015

Status

approved