A189047 Semiprimes which are one more than a perfect power.

9, 10, 26, 33, 65, 82, 122, 129, 145, 217, 226, 362, 485, 626, 785, 842, 901, 1157, 1226, 1522, 1765, 1937, 2026, 2049, 2117, 2305, 2402, 2501, 2602, 2705, 3365, 3482, 3601, 3722, 3845, 4097, 4226, 4762, 5042, 5777, 5833, 6085, 6242, 6401, 7226, 7397, 7745, 8193, 8465, 9026, 9217

Offset: 1

Author

Jonathan Vos Post, Apr 15 2011

Keywords

• easy
• nonn

Comments

Numbers of the form p*q where p and q are primes, not necessarily distinct, such that p*q - 1 is a perfect power (squares, cubes, etcetera). T. D. Noe suggested the name semiprimes which are super-perfect powers.

The number of terms <= 10^k: 2, 6, 17, 51, 131, 379, 1015, 2865, 8086, ..., . - Robert G. Wilson v, Apr 16 2011

Examples

			a(21) = 42^2 + 1 = 1765 = 5 * 353.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..8086

Crossrefs

Cf. A001358, A001597, A045542, A177955, A189045.

Programs

Mathematica

fQ[n_] := GCD @@ Last /@ FactorInteger[n - 1] > 1 && Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Apr 16 2011 *)

Formula

A001358 INTERSECTION {A001597 + 1}.