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

1,1

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

Links

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

Formula

A001358 INTERSECTION {A001597 + 1}.

Example

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

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 *)

Crossrefs

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

Sequence in context: A320728 A111033 A123048 * A041170 A041168 A042635

Adjacent sequences: A189044 A189045 A189046 * A189048 A189049 A189050

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 15 2011

Status

approved