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%I #15 Apr 21 2026 09:07:01
%S 4,9,25,49,169,289,361,961,3721,7921,11449,16129,271441,368449,
%T 1635841,4853209,5202961,10349089,18088009,19562929,93876721,98823481,
%U 125731369,397483969,470933401,538657681,1979983009,7437855049,12210913009,17436938401,46695320281,572805271921,738625081489
%N Squares of Mersenne prime exponents A000043.
%C 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.
%F a(n) = A000043(n)^2 = A000290(A000043(n)).
%t MersennePrimeExponent[Range[35]]^2 (* _Paolo Xausa_, Apr 21 2026 *)
%o (PARI)
%o 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 */
%o 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
%Y Cf. A000043 (Mersenne prime exponents), A000290 (the squares), A085724 (2^k - 1 is semiprime).
%K nonn
%O 1,1
%A _M. F. Hasler_, Apr 15 2026