A083348 Numbers k such that r(k) = Sum(e/p: k = Product(p^e)) > 1.

8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 90, 92, 96, 100, 104, 108, 112, 116, 120, 124, 126, 128, 132, 135, 136, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 198

Offset

1,1

Comments

The number of terms not exceeding 10^m, for m = 1, 2, ..., are 1, 29, 318, 3174, 31763, 317813, 3177179, 31774009, 317745099, 3177373819, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3177... . - Amiram Eldar, Jun 24 2022

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

A083345(a(n)) > A083346(a(n)).

A083345(A051674(n)) = A083346(A051674(n)).

A083345(A083347(n)) < A083346(A083347(n)).

A168036(a(n)) > 0. - Reinhard Zumkeller, May 22 2015

Mathematica

ad[n_] := Switch[n, 0 | 1, 0, _, If[PrimeQ[n], 1, Sum[Module[ {p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];
Select[Range[1000], ad[#] > # &] (* Jean-François Alcover, May 04 2023 *)

Prog

(Haskell)
a083348 n = a083348_list !! (n-1)
a083348_list = filter ((> 0) . a168036) [1..]
-- Reinhard Zumkeller, May 22 2015, May 10 2011

Crossrefs

Cf. A003415, A072873, A051674, A083345, A083346, A083347, A168036, A369048 (characteristic function), A369049.

Subsequence of A100717.

Sequence in context: A091375 A282671 A192991 * A174261 A063539 A253296

Adjacent sequences: A083345 A083346 A083347 * A083349 A083350 A083351

Keyword

nonn

Author

Reinhard Zumkeller, Apr 25 2003

Status

approved