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A317478
Triangular numbers whose sum of divisors is an oblong number.
1
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
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
Intersection of A000217 and A236387. - Michel Marcus, Jul 30 2018
Sequence in context: A091307 A254879 A298168 * A353901 A081537 A058007
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 29 2018
STATUS
approved