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

1, 6, 510510, 13082761331670030, 40729680599249024150621323470, 2566376117594999414479597815340071648394470

Offset: 1

Author

Antti Karttunen, Feb 07 2024

Keywords

• nonn

Comments

Primorials A002110(k) such that A003415(A002110(k)) [= A024451(k)] is a multiple of A000040(1+k).

a(7) = A002110(261202), which is too large to include here, or even in a b-file.

Examples

			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.
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.
		

Links

• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000040, A002110, A003415, A024451, A293457 (the corresponding primes), A369972.

Subsequence of A369970.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A024451(n) = numerator(sum(i=1, n, 1/prime(i)));
isA369972(n) = !(A024451(n)%prime(1+n));
for(n=0,2^10,if(isA369972(n),print1(A002110(n),", ")));

Formula

a(n) = A002110(A369972(n)).