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

1, 6, 510510, 13082761331670030, 40729680599249024150621323470, 2566376117594999414479597815340071648394470

Offset

1,2

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.

Links

Table of n, a(n) for n=1..6.

Index entries for sequences related to primorial numbers

Formula

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

Example

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.

Prog

(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), ", ")));

Crossrefs

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

Subsequence of A369970.

Sequence in context: A067503 A079288 A072234 * A172823 A182791 A336397

Adjacent sequences: A369970 A369971 A369972 * A369974 A369975 A369976

Keyword

nonn

Author

Antti Karttunen, Feb 07 2024

Status

approved