A115904 -id:A115904 - cp's OEIS frontend

A115909 Numbers k such that sigma(k)*k is a triangular number.

1, 2, 4, 8, 16, 32, 57, 64, 65, 85, 87, 128, 256, 512, 1024, 1245, 1421, 2048, 3146, 3330, 3790, 4096, 6695, 7257, 8192, 10137, 16384, 25884, 32768, 34420, 34551, 34947, 65536, 131072, 208495, 262144, 348161, 440495, 524288, 530270, 534430

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

Infinite, since all the powers of 2 belong to the sequence.

			sigma(1421)*1421 = 2429910 = T(2204).

Amiram Eldar, Table of n, a(n) for n = 1..100

Cf. A064987, A000217, A115904, A115910.

Select[Range[540000],IntegerQ[(Sqrt[1+8(#*DivisorSigma[1,#])]-1)/2]&] (* Harvey P. Dale, Dec 16 2011 *)

isok(n) = ispolygonal(n*sigma(n), 3); \\ Amiram Eldar, Apr 06 2023

A115906 Numbers k such that k + sigma(k) + phi(k) is a triangular number.

Original entry on oeis.org

1, 2, 5, 7, 9, 16, 144, 186, 410, 656, 680, 805, 963, 968, 1152, 1331, 1419, 1476, 1557, 1608, 2158, 2220, 2376, 2401, 2529, 2840, 3376, 3447, 3570, 3591, 4018, 5030, 5769, 5967, 6530, 6720, 6854, 6955, 7250, 7856, 8004, 8514, 8946, 9144

Offset: 1

Giovanni Resta, Feb 06 2006

nonn

			1331 + sigma(1331) + phi(1331) = 4005 = T(89).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000010, A000203, A000217, A069066, A115904, A115905.

isok(n) = {my(f=factor(n)); ispolygonal(n + sigma(f) + eulerphi(f), 3);} \\ Amiram Eldar, Apr 06 2023

cp's OEIS Frontend

A115909 Numbers k such that sigma(k)*k is a triangular number.

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