A115904 -id:A115904

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A115909

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A064987, A000217, A115904, A115910.

KEYWORD

nonn

AUTHOR

Giovanni Resta, Feb 06 2006

STATUS

approved

A115906

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

+10
1

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