A236387 -id:A236387 - cp's OEIS frontend

A317478 Triangular numbers whose sum of divisors is an oblong number.

6, 28, 55, 496, 666, 780, 1540, 2145, 6441, 6903, 8128, 15051, 21736, 36585, 44551, 232903, 234955, 644680, 2258875, 3186550, 3462396, 6211050, 22174470, 33550336, 48437403, 62591266, 107538445, 134898525, 153554050, 624157446, 1309312378, 1339937028

Offset: 1

Amiram Eldar, Jul 29 2018

Includes all the even perfect numbers.
The indices of these triangular numbers are 3, 7, 10, 31, 36, 39, 55, 65, 113, 117, 127, 173, 208, 270, 298, 682, 685, 1135, 2125, 2524, 2631, 3524, 6659, 8191, 9842, 11188, 14665, 16425, 17524, 35331, 51172, 51767, 52019, 52486, 58993, 65585, 97532.
The indices of the corresponding oblong numbers are 3, 7, 8, 31, 38, 48, 63, 63, 95, 104, 127, 144, 224, 255, 224, 512, 575, 1215, 1728, 2448, 3072, 3968, 7695, 8191, 9215, 9792, 12159, 15872, 17576, 37296, 46656, 58239, 63855, 40959, 46080, 62720, 102960.
Number of terms < 10^k, k=1,2,3...: 1, 3, 6, 11, 15, 18, 22, 26, 30, 40, 52, 64, 80, 90, 110, 128, ..., . - Robert G. Wilson v, Jul 31 2018

			55 is in the sequence since sigma(55) = 72 = 8 * 9 is an oblong number.

Robert G. Wilson v, Table of n, a(n) for n = 1..129

Cf. A000203, A000217, A000396, A002378, A083674, A083675, A175849.

Intersection of A000217 and A236387. - Michel Marcus, Jul 30 2018

tri[n_] := n(n+1)/2; aQ[n_] := IntegerQ[Sqrt[4 * DivisorSigma[1, tri[n]] + 1]]; tri[Select[Range[52000], aQ]]
Module[{nn=60000,obno},obno=Table[n(n+1),{n,nn}];Select[Accumulate[Range[nn]],MemberQ[ obno,DivisorSigma[1,#]]&]] (* Harvey P. Dale, Aug 26 2024 *)

cp's OEIS Frontend

A317478 Triangular numbers whose sum of divisors is an oblong number.

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