A361386 Infinitary arithmetic numbers: numbers for which the arithmetic mean of the infinitary 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, 48, 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

Offset

1,2

Comments

Number k such that A037445(k) divides A049417(k).

Subsequence of the unitary arithmetic numbers (A103826).

Links

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

Formula

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

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, (1 + p^(2^(m - j)))/2, 1], {j, 1, m}]]; q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[100], q]

Prog

(PARI) is(n) = {my(f = factor(n), b); denominator(prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], (f[i, 1]^(2^(#b-k))+1)/2, 1)))) == 1; }

Crossrefs

Cf. A037445, A049417, A077609.

Similar sequences: A003601, A103826.

Sequence in context: A390677 A356844 A103826 * A361786 A079905 A321321

Adjacent sequences: A361383 A361384 A361385 * A361387 A361388 A361389

Keyword

nonn

Author

Amiram Eldar, Mar 10 2023

Status

approved