A341214 a(n) is the smallest prime p such that p, p - 1, p - 2, ..., p - n + 1 have 2, 4, 6, ..., 2*n divisors respectively.

2, 7, 47, 1019, 55414379

Offset: 1

Author

Jaroslav Krizek, Feb 07 2021

Keywords

• nonn
• fini
• full

Comments

a(n) is the smallest prime p such that tau(p) = tau(p - 1)/2 = tau(p - 2)/3 = ... = tau(p - n + 1)/n = 2, where tau(k) = the number of divisors of k (A000005).

No such prime p exists for n > 5, so a(5) is the final term. - Jon E. Schoenfield, Feb 07 2021

Examples

			a(4) = 1019 because 1016, 1017, 1018 and 1019 have 8, 6, 4, and 2 divisors respectively and there is no smaller prime having this property (see A340872).
		

Links

• Jon E. Schoenfield, A proof that a(5) is the final term

Crossrefs

Cf. A341213 (similar sequence for natural numbers).

Cf. A000005, A294528, A340871, A340872.