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A189047 Semiprimes which are one more than a perfect power. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)