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%I #25 Aug 06 2024 11:29:54
%S 8,18,24,50,64,81,98,160,242,324,338,375,384,578,722,896,1029,1058,
%T 1215,1682,1922,2048,2500,2738,3362,3698,3993,4374,4418,4608,5618,
%U 6591,6962,7442,8978,9604,10082,10240,10658,12482,13778,14739,15309,15625,15842,18818
%N Numbers of the form k*p^k, where k>1 and p is a prime.
%C Each term in this sequence has a single presentation in the form k*p^k.
%H Amiram Eldar, <a href="/A352081/b352081.txt">Table of n, a(n) for n = 1..10000</a>
%H Peter Lindqvist and Jaak Peetre, <a href="https://citeseerx.ist.psu.edu/pdf/0ff00f98eb25cbd076cf7a18f85ae51e4b95f618">On the remainder in a series of Mertens</a>, Expositiones Mathematicae, Vol. 15 (1997), pp. 467-478. See eq. (3).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MertensConstant.html">Mertens Constant</a>. See eq. (5).
%F 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).
%e 8 is a term since 8 = 2*2^2.
%e 18 is a term since 18 = 2*3^2.
%e 24 is a term since 24 = 3*2^3.
%t 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]
%Y Subsequences: A036289 \ {0, 2}, A036290 \ {0, 3}, A036291 \ {0, 5}, A036293 \ {0, 7}, A073113 \ {2}, A079704, A100042, A104126.
%Y Cf. A001620, A077761, A143524.
%K nonn,changed
%O 1,1
%A _Amiram Eldar_, Apr 16 2022
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