A341812 -id:A341812 - cp's OEIS frontend

A341805 Numbers k such that (product of first k primes)-1 is divisible by the (k+1)-th prime.

0, 2, 4, 9823712

Offset: 1

Jeppe Stig Nielsen, Feb 20 2021

			4 is a member because 2*3*5*7-1 (product of first 4 primes, minus one) is divisible by the 5th prime, 11.
9823712 is a member because 2*3*5*...*176078267-1 is divisible by 176078293, where 176078267 is the 9823712th prime.

Cf. A079276, A081618, A338543, A341804, A341812.

isok(k) = ((vecprod(primes(k)) - 1) % prime(k+1)) == 0; \\ Michel Marcus, Mar 03 2021

a(n) = A000720(A341804(n)) - 1.

A341804 Primes p dividing (the product of the primes less than p)-1.

Original entry on oeis.org

2, 5, 11, 176078293

Offset: 1

Jeppe Stig Nielsen, Feb 20 2021

The initial term 2 is included because the empty product minus 1 (which gives zero) is divisible by 2.

			The prime 11 is included because 2*3*5*7-1 is divisible by 11. Therefore, the last factor of the product, namely 7, is in A341812.

Cf. A058233, A066735, A341805, A341812.

t=1;forprime(p=2,,((t-1)%p==0)&&print1(p,", ");t*=p)

cp's OEIS Frontend

A341805 Numbers k such that (product of first k primes)-1 is divisible by the (k+1)-th prime.

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