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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
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.
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)))}
KEYWORD
nonn,changed
AUTHOR
Antonio Roldán, Mar 16 2015
STATUS
approved