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%I #19 Feb 10 2024 18:57:56
%S 0,2,7,14,21,28,261202
%N Numbers k such that (prime(k)#)' is a multiple of prime(1+k), where prime(k)# means the k-th primorial, A002110(k), and ' stands for taking the arithmetic derivative, A003415.
%C Numbers k for which A024451(k) is a multiple of A000040(1+k).
%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F a(n) = A000720(A293457(n)) - 1.
%e 7 is included because the primorial prime(7)# = A002110(7) = 510510 has as its arithmetic derivative 510510' = A024451(7) = 716167 = 19*37693, which is divisible by the next larger prime not present in the primorial, in this case by prime(8) = 19.
%o (PARI)
%o A024451(n) = numerator(sum(i=1, n, 1/prime(i)));
%o isA369972(n) = !(A024451(n)%prime(1+n));
%Y Cf. A000040, A000720, A024451, A293457 (corresponding primes), A369970, A369973 (corresponding primorials).
%Y Cf. also A109628.
%K nonn,more,hard
%O 1,2
%A _Antti Karttunen_, Feb 07 2024
%E Found a(7) by computing it as A000720(A293457(7))-1. - _Antti Karttunen_, Feb 08 2024