A069164 -id:A069164 - cp's OEIS frontend

A069165 a(n) are the integers corresponding to A069164(n).

1, 3, 33, 55, 75, 77, 121, 125, 121, 143, 175, 187, 275, 209, 274, 275, 253, 325, 319, 341, 425, 407, 475, 588, 451, 473, 575, 517, 583, 725, 649, 1233, 671, 775, 737, 781, 803, 925, 869, 1025, 913, 1075, 979, 1175, 1067, 1111, 1133, 1325, 1177, 2055, 1199

Offset: 1

Benoit Cloitre, Apr 09 2002

The previous name was "Integers of the form k * Sum_{d|k} 1/tau(d)", but this did not take into account the occurrence of multiple terms and the non-ascending order.

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

Cf. A000005, A069164, A265391, A265392.

Select[Table[n * DivisorSum[n, 1/DivisorSigma[0, #] &], {n, 1, 500}], IntegerQ] (* Amiram Eldar, Apr 29 2025 *)

a(n) = f(A069164(n)), where f(n) = n*A265391(n)/A265392(n). - Amiram Eldar, Apr 29 2025

Name corrected by Hugo Pfoertner, Jul 07 2024

A069166 Numbers k such that k*Sum_{d|k} 1/sigma(d) is an integer.

Original entry on oeis.org

1, 6, 14, 40, 120, 244, 280, 440, 494, 680, 920, 1220, 2040, 2840, 2968, 3480, 6360, 9880, 10680, 16376, 20618, 25160, 32280, 34720, 40136, 40280, 42136, 45560, 45994, 46280, 85880, 91160, 120408, 200680, 213280, 231080, 242840, 377080, 410552, 412360, 421480, 441496, 447320

Offset: 1

Benoit Cloitre, Apr 09 2002

Amiram Eldar, Table of n, a(n) for n = 1..300

Cf. A069164.

Select[Range[125000],IntegerQ[# Total[1/DivisorSigma[1,Divisors[#]]]]&] (* Harvey P. Dale, Nov 03 2017 *)

isok(k) = denominator(k*sumdiv(k, d, 1/sigma(d))) == 1; \\ Michel Marcus, Feb 15 2021

More terms from Michel Marcus, Feb 15 2021

cp's OEIS Frontend

A069165 a(n) are the integers corresponding to A069164(n).

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