A333639 Numbers m such that g(m) = (m * tau(m) / sigma(m)), h(m) = (m * sigma(m)) / tau(m) and k(m) = (tau(m) * sigma(m)) / m are all integers.

1, 6, 672, 1638, 30240, 32760, 2178540, 17428320, 23569920, 29410290, 45532800, 714954240, 1379454720, 14182439040, 19209881600, 30600708096, 51001180160, 57575890944, 57629644800, 153003540480, 206166804480, 403031236608, 465036042240, 482476262400

Offset

1,2

Comments

Corresponding sequences of values of integers g(m), h(m) and k(m): {1, 2, 8, 9, 24, 24, 54, 96, 80, 81, 96, 200, ...}, {1, 18, 56448, 298116, 38102400, 44717400, 87889565400, 3164024354400, ...}, {1, 8, 72, 64, 384, 384, 864, 1944, 1280, 1024, 1536, 4608, 2304, 9600, 2916, ...}.

Links

Table of n, a(n) for n=1..24.

Mathematica

Select[Range[10^5], Divisible[# * (d = DivisorSigma[0, #]), (s = DivisorSigma[1, #])] && Divisible[# * s, d] && Divisible[d * s, #] &] (* Amiram Eldar, Mar 31 2020 *)

Prog

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

Crossrefs

Subsequence of harmonic numbers (A001599).

Intersection of A001599, A333638 and A071707.

Cf. A000005, A000203.

Sequence in context: A222720 A309597 A269842 * A331724 A046985 A159371

Adjacent sequences: A333636 A333637 A333638 * A333640 A333641 A333642

Keyword

nonn

Author

Jaroslav Krizek, Mar 30 2020

Status

approved