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The second arithmetic derivative of primorial numbers.
4

%I #8 Jan 31 2024 16:55:59

%S 0,0,1,1,32,1,1,37712,381596,9835475,36880858,5221912091,149759057759,

%T 186024798,456607833524310,655374897748042,32188411533060,

%U 3002590335363139484,1,1,1489192548103758778136571,905624730150525686386253700,1,110832638787270947169636975150,331748330219014906068858,349669183443106226663011852002384

%N The second arithmetic derivative of primorial numbers.

%C See comments in A024451.

%H Antti Karttunen, <a href="/A369651/b369651.txt">Table of n, a(n) for n = 0..49</a>

%F a(n) = A003415(A024451(n)) = A068346(A002110(n)).

%o (PARI)

%o A002110(n) = prod(i=1,n,prime(i));

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A369651(n) = A003415(A003415(A002110(n)));

%Y Cf. A002110, A003415, A024451, A068346, A109628 (positions of 1's).

%Y Cf. also A368702.

%K nonn

%O 0,5

%A _Antti Karttunen_, Jan 31 2024