A395178 Squares of Mersenne prime exponents A000043.

4, 9, 25, 49, 169, 289, 361, 961, 3721, 7921, 11449, 16129, 271441, 368449, 1635841, 4853209, 5202961, 10349089, 18088009, 19562929, 93876721, 98823481, 125731369, 397483969, 470933401, 538657681, 1979983009, 7437855049, 12210913009, 17436938401, 46695320281, 572805271921, 738625081489

Offset

1,1

Comments

Numbers k such that 2^k - 1 is a semiprime (cf. A085724) can only be primes that are not Mersenne prime exponents, or squares of Mersenne prime exponents; i.e., in this sequence.

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = A000043(n)^2 = A000290(A000043(n)).

Mathematica

MersennePrimeExponent[Range[35]]^2 (* Paolo Xausa, Apr 21 2026 *)

Prog

(PARI)
A395178(n)=A000043(n)^2 /* where {A000043(n)=A43[n]} could fetch the values from a list, or create the list itself using is_A000043 */
forprime(p=2, oo, is_A000043(p) && print1(p^2", ")) \\ with is_A000043(p)=ispseudorpime(2^p-1) or better Lucas-Lehmer test given there

Crossrefs

Cf. A000043 (Mersenne prime exponents), A000290 (the squares), A085724 (2^k - 1 is semiprime).

Sequence in context: A133019 A376746 A326708 * A028866 A146981 A068373

Adjacent sequences: A395175 A395176 A395177 * A395179 A395180 A395181

Keyword

nonn

Author

M. F. Hasler, Apr 15 2026

Status

approved