A333638 Numbers m such that (m * sigma(m)) / tau(m) is an integer k.

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset

1,2

Comments

Corresponding values of integers k: 1, 3, 6, 15, 18, 28, 30, 39, 45, 66, 56, 91, 84, 90, 153, 117, 190, 140, 168, ...

Supersequence of refactorable (A033950), arithmetic (A003601) and refactorable arithmetic numbers (A047727).

Sequence of numbers from this sequence that are neither refactorable nor arithmetic: 10, 26, 32, 34, 50, 58, 63, 74, 75, 82, 90, 98, 106, 117, 120, 122, 130, 146, ...

Links

Table of n, a(n) for n=1..67.

Example

10 is a term because (10 * sigma(10)) / tau(10) = (10 * 18) / 4 = 45 (integer).

Mathematica

Select[Range[100], Divisible[# * DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Mar 31 2020 *)

Prog

(Magma) [m: m in [1..10^5] | IsIntegral((&+Divisors(m) * m) / #Divisors(m))]
(PARI) isok(m) = (m*sigma(m) % numdiv(m)) == 0; \\ Michel Marcus, Mar 31 2020

Crossrefs

Cf. A000005, A000203, A033950, A047727.

Sequence in context: A293754 A242410 A258022 * A089590 A052406 A022306

Adjacent sequences: A333635 A333636 A333637 * A333639 A333640 A333641

Keyword

nonn

Author

Jaroslav Krizek, Mar 30 2020

Status

approved