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Convolution of natural numbers with (1, p(1), p(2), ... ), where p(k) is the k-th prime.
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%I #14 Jul 11 2020 02:29:42

%S 1,4,10,21,39,68,110,169,247,348,478,639,837,1076,1358,1687,2069,2510,

%T 3012,3581,4221,4934,5726,6601,7565,8626,9788,11053,12425,13906,15500,

%U 17221,19073,21062,23190,25467,27895,30480,33228,36143,39231,42498,45946,49585

%N Convolution of natural numbers with (1, p(1), p(2), ... ), where p(k) is the k-th prime.

%H F. Javier de Vega, <a href="https://arxiv.org/abs/2003.13378">An extension of Furstenberg's theorem of the infinitude of primes</a>, arXiv:2003.13378 [math.NT], 2020.

%F a(n) = Sum_{k<=n} [(A158611(k+1)) * (A000027(n-k+1))] = Sum_{k<=n} [(A008578(k)) * (A000027(n-k+1))]. [_Jaroslav Krizek_, Aug 05 2009; Correction for change of offset in A158611 and A008578 in Aug 2009 _Jaroslav Krizek_, Jan 27 2010]

%t Nest[Accumulate,Join[{1},Select[Range@200,PrimeQ]],2] (* _Vladimir Joseph Stephan Orlovsky_, Jan 25 2012 *)

%Y Cf. A007504, A014148, A014150, A014284, A023538, A178138.

%K nonn

%O 1,2

%A _Clark Kimberling_