cp's OEIS Frontend

A369973 Primorials whose arithmetic derivative is divisible by the next larger prime not present in that primorial.

%I A369973 #26 Feb 10 2024 18:58:04
%S A369973 1,6,510510,13082761331670030,40729680599249024150621323470,
%T A369973 2566376117594999414479597815340071648394470
%N A369973 Primorials whose arithmetic derivative is divisible by the next larger prime not present in that primorial.
%C A369973 Primorials A002110(k) such that A003415(A002110(k)) [= A024451(k)] is a multiple of A000040(1+k).
%C A369973 a(7) = A002110(261202), which is too large to include here, or even in a b-file.
%H A369973 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A369973 a(n) = A002110(A369972(n)).
%e A369973 The zeroth primorial, 1 = A002110(0), is included, because its arithmetic derivative 1' = A024451(0) = 0 is divisible by the next larger prime not present in the primorial, in this case by prime(1) = 2.
%e A369973 The primorial 510510 = prime(7)# is included, because its arithmetic derivative 510510' = A024451(7) = 716167 = 19*37693 is divisible by the next larger prime not present in the primorial, in this case by prime(8) = 19.
%o A369973 (PARI)
%o A369973 A002110(n) = prod(i=1,n,prime(i));
%o A369973 A024451(n) = numerator(sum(i=1, n, 1/prime(i)));
%o A369973 isA369972(n) = !(A024451(n)%prime(1+n));
%o A369973 for(n=0,2^10,if(isA369972(n),print1(A002110(n),", ")));
%Y A369973 Cf. A000040, A002110, A003415, A024451, A293457 (the corresponding primes), A369972.
%Y A369973 Subsequence of A369970.
%K A369973 nonn
%O A369973 1,2
%A A369973 _Antti Karttunen_, Feb 07 2024