A175849 -id:A175849 - cp's OEIS frontend

A175850 Numbers m with property that m-th triangular number is a sum of divisors of some k-th triangular number (A175849).

1, 13, 12, 384, 575, 783, 4095, 4607, 4095, 6912, 12543, 13824, 16895, 21504, 20735, 27264, 40959, 68256, 76544, 104832, 175104, 130559, 146432, 180224, 129024, 202239, 316224, 328320, 372735, 395199, 512000, 532575, 512000, 732159, 787968, 1181439, 1756160, 2253824

Offset: 1

Zak Seidov, Sep 27 2010

nonn

			Some pairs of k,m: 1,1; 8,13; 9,12; 215,384; 458,575; 520,783; 2232,4095; 3251,4607; 3634,4095; 5349,6912; 9489,12543; 10051,13824.

Amiram Eldar, Table of n, a(n) for n = 1..226
Zak Seidov, Table of values of n, m
Zak Seidov, A175849,A175850

Cf. A000203 (sigma(n) = sum of divisors of n), A000217 (triangular numbers), A175849 (corresponding values of n).

f[n_] := Sqrt[8*DivisorSigma[1, n*(n+1)/2] + 1]; (f /@ Select[Range[10^4], IntegerQ @ f[#] &] - 1)/2 (* Amiram Eldar, Feb 23 2020 *)

{for(n=1, 10^7, m=sigma(n*(n+1)/2); issquare(d=1+8*m) && print1((sqrtint(d)-1)/2, ", "))} \\ edited by Michel Marcus, Feb 23 2020

sigma(T(k)) = T(m); A000203(A000217(k)) = A000217(m).

Data corrected and extended by Amiram Eldar, Feb 23 2020

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

Original entry on oeis.org

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

A175850 Numbers m with property that m-th triangular number is a sum of divisors of some k-th triangular number (A175849).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions