A361786 Bi-unitary arithmetic numbers: numbers for which the arithmetic mean of the bi-unitary divisors is an integer.

1, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 83, 84, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99

Offset

1,2

Comments

First differs from A361386 at n = 35.

Number k such that A286324(k) divides A188999(k).

Links

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

Example

6 is a term since the arithmetic mean of its bi-unitary divisors, {1, 2, 3, 6}, is 3 which is an integer.

Mathematica

f[p_, e_] := If[OddQ[e], (p^(e+1)-1)/((e + 1)*(p-1)), ((p^(e+1)-1)/(p-1)-p^(e/2))/e]; q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[100], q]

Prog

(PARI) is(n) = {my(f = factor(n), p, e); denominator(prod(i=1, #f~, p = f[i, 1]; e = f[i, 2]; if(e%2, (p^(e+1)-1)/((e + 1)*(p-1)), ((p^(e+1)-1)/(p-1)-p^(e/2))/e))) == 1; }

Crossrefs

Cf. A188999, A222266, A286324.

Similar sequences: A003601, A103826, A361386.

Sequence in context: A356844 A103826 A361386 * A079905 A321321 A154611

Adjacent sequences: A361783 A361784 A361785 * A361787 A361788 A361789

Keyword

nonn

Author

Amiram Eldar, Mar 24 2023

Status

approved