A082869 -id:A082869 - cp's OEIS frontend

A280149 Numbers k such that 3^k - 2^k is not squarefree.

10, 11, 20, 22, 30, 33, 40, 42, 44, 50, 52, 55, 57, 60, 66, 70, 77, 80, 84, 88, 90, 99, 100, 104, 110, 114, 120, 121, 126, 130, 132, 140, 143, 150, 154, 156, 160, 165, 168, 170, 171, 176, 180, 187, 190, 198, 200, 203, 208, 209, 210, 220, 228, 230, 231, 240, 242, 250, 252, 253, 260, 264, 270, 272, 275, 280, 285

Offset: 1

Juri-Stepan Gerasimov, Dec 27 2016

nonn

Primitive members (not multiples of earlier terms) are 10, 11, 42, 52, 57, 203, 272, 497, .... - Juri-Stepan Gerasimov and Charles R Greathouse IV, Dec 27 2016
From Robert Israel, Dec 27 2016: (Start)
Numbers divisible by the order of 3/2 mod p^2 for some prime p > 3.
Includes numbers divisible by p^2-p for some prime p > 3.
If k is a member, then so are all multiples of k. (End)

			10 is in this sequence because 3^10 - 2^10 = 58025 = 5^2*11*211.

Charles R Greathouse IV and Amiram Eldar, Table of n, a(n) for n = 1..134 (terms 1..127 from Charles R Greathouse IV)

Cf. A001047, A005117, A013929, A049094, A057468, A082869, A282688, A282689.

[n: n in [1..156] | not IsSquarefree(3^n-2^n)];

Select[Range@ 120, ! SquareFreeQ[3^# - 2^#] &] (* Michael De Vlieger, Dec 27 2016 *)

is(n)=issquarefree(3^n-2^n)==0 \\ Charles R Greathouse IV, Dec 27 2016

More terms from Charles R Greathouse IV, Dec 27 2016

A095027 Semiprimes of the form 3^n - 2^n.

Original entry on oeis.org

65, 2059, 19171, 1586131, 1161737179, 94134790219, 450283768452043891, 7509466514977363620705281135650699, 2909321189362570189660446183802104997118371, 19088056323407826916968161259086927505582748291

Offset: 1

Hugo Pfoertner, Jun 03 2004

nonn

			a(1)=65 because 3^4-2^4=65=5*13 is a semiprime; a(3)=19171: 3^9-2^9=19171=19*1009.

Dario Alpern, Factorization using the Elliptic Curve Method

Cf. A082869 = n such that 3^n-2^n is a semiprime, A058765 primes of the form 3^n-2^n.

IsSemiprime:=func; [s: n in [2..100] | IsSemiprime(s) where s is 3^n - 2^n]; // Vincenzo Librandi, Sep 21 2012

Select[Table[3^n - 2^n, {n, 100}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 21 2012 *)

a(10) from Vincenzo Librandi, Sep 21 2012

A381725 Numbers k such that 5^k - 4^k is a semiprime.

Original entry on oeis.org

2, 5, 7, 11, 13, 19, 31, 41, 79, 83, 113, 157, 173, 233, 281, 317, 359, 373

Offset: 1

Zak Seidov and Robert Israel, Mar 05 2025

Are all terms prime? Any term that is not a prime must be the square of a member of A059802.

			a(3) = 7 is a term because 5^7 - 4^7 = 61741 = 29 * 2129 with 29 and 2129 prime.

Status of 5^449-4^449 in factordb.com.

Cf. A001222, A001358, A005060, A059802, A082869.

filter:= n -> numtheory:-bigomega(5^n - 4^n):
select(filter, [2,seq(i,i=3..120,2]);

A001222(A005060(a(n))) = 2.

a(14)-a(18) from Jinyuan Wang, Mar 05 2025

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A280149 Numbers k such that 3^k - 2^k is not squarefree.

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A095027 Semiprimes of the form 3^n - 2^n.

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A381725 Numbers k such that 5^k - 4^k is a semiprime.

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