A356743 Numbers k such that k and k+2 both have exactly 6 divisors.

18, 50, 242, 243, 423, 475, 603, 637, 722, 845, 925, 1682, 1773, 2007, 2523, 2525, 2527, 3123, 3175, 3177, 4203, 4475, 4525, 4923, 5823, 6725, 6811, 6962, 7299, 7442, 7675, 8425, 8957, 8973, 9457, 9925, 10051, 10082, 10467, 11673, 11709, 12427, 12482, 12591, 13023, 13075

Offset: 1

Author

Jianing Song, Aug 25 2022

Keywords

• nonn

Comments

If an even number has exactly 6 divisors, then it is of the form 32, 4*p or 2*p^2 for an odd prime p. Note that 4*p + 2 = 2*q^2 is impossible since q^2 - 1 is divisible by 24 for prime q >= 5. As a result, if k is an even term, then it is of the form 2*p^2 such that (p^2+1)/2 is a prime (p is in A048161).

Examples

			50 is a term since 50 and 52 both have 6 divisors.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048161.

Numbers k such that k and k+2 both have exactly m divisors: A001359 (m=2), A356742 (m=4), this sequence (m=6), A356744 (m=8).

Cf. also A049103 (numbers k such that k and k+1 both have exactly 6 divisors).

Programs

PARI

isA356743(n) = numdiv(n)==6 && numdiv(n+2)==6