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

Author

Antonio Roldán, Mar 16 2015

Keywords

• nonn

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.

Examples

			2 is in the sequence because 2=1*2 is oblong, and sigma(2) = 1+2 = 3 = 2*3/2 is triangular.
		

Crossrefs

Cf. A000217, A002378, A139256, A045746, A256149, A256151, A256152.

Programs

Mathematica

Select[2 Accumulate[Range@10000], MemberQ[Accumulate[Range@10000], DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 17 2015 *)

PARI

{for (i=1,i=10^6,n=i*(i+1);if(ispolygonal(sigma(n), 3),print(n)))}