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

Author

Jaroslav Krizek, Mar 30 2020

Keywords

• nonn

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, ...

Examples

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

Crossrefs

Cf. A000005, A000203, A033950, A047727.

Programs

Magma

[m: m in [1..10^5] | IsIntegral((&+Divisors(m) * m) / #Divisors(m))]

Mathematica

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

PARI

isok(m) = (m*sigma(m) % numdiv(m)) == 0; \\ Michel Marcus, Mar 31 2020