A352081 Numbers of the form k*p^k, where k>1 and p is a prime.

8, 18, 24, 50, 64, 81, 98, 160, 242, 324, 338, 375, 384, 578, 722, 896, 1029, 1058, 1215, 1682, 1922, 2048, 2500, 2738, 3362, 3698, 3993, 4374, 4418, 4608, 5618, 6591, 6962, 7442, 8978, 9604, 10082, 10240, 10658, 12482, 13778, 14739, 15309, 15625, 15842, 18818

Offset: 1

Author

Amiram Eldar, Apr 16 2022

Keywords

• nonn

Comments

Each term in this sequence has a single presentation in the form k*p^k.

Examples

			8 is a term since 8 = 2*2^2.
18 is a term since 18 = 2*3^2.
24 is a term since 24 = 3*2^3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Peter Lindqvist and Jaak Peetre, On the remainder in a series of Mertens, Expositiones Mathematicae, Vol. 15 (1997), pp. 467-478. See eq. (3).
• Eric Weisstein's World of Mathematics, Mertens Constant. See eq. (5).

Crossrefs

Subsequences: A036289 \ {0, 2}, A036290 \ {0, 3}, A036291 \ {0, 5}, A036293 \ {0, 7}, A073113 \ {2}, A079704, A100042, A104126.

Cf. A001620, A077761, A143524.

Programs

Mathematica

addP[p_, n_] := Module[{k = 2, s = {}, m}, While[(m = k*p^k) <= n, k++; AppendTo[s, m]]; s]; seq[max_] := Module[{m = Floor[Sqrt[max/2]], s = {}, ps}, ps = Select[Range[m], PrimeQ]; Do[s = Join[s, addP[p, max]], {p, ps}]; Sort[s]]; seq[2*10^4]

Formula

Sum_{n>=1} 1/a(n) = -A143524 = gamma - B_1, where gamma is Euler's constant (A001620), and B_1 is Mertens's constant (A077761).