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

1,1

Comments

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

Links

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

Example

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

Mathematica

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 *)

Crossrefs

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

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

Sequence in context: A091307 A254879 A298168 * A353901 A081537 A058007

Adjacent sequences: A317475 A317476 A317477 * A317479 A317480 A317481

Keyword

nonn,easy

Author

Amiram Eldar, Jul 29 2018

Status

approved