A354179 Numbers whose square has a number of divisors that is coprime to 30.

1, 8, 27, 32, 64, 125, 216, 243, 256, 343, 512, 729, 864, 1000, 1331, 1728, 1944, 2048, 2197, 2744, 3125, 3375, 4000, 4913, 5832, 6561, 6859, 6912, 7776, 8000, 9261, 10648, 10976, 12167, 13824, 15552, 15625, 16384, 16807, 17576, 19683, 21952, 23328, 24389, 25000

Offset: 1

Author

Amiram Eldar, May 18 2022

Keywords

• nonn

Comments

Numbers k such that gcd(d(k^2), 30) = 1, where d(k) is the number of divisors of k (A000005).

Examples

			8 is a term since A000005(8^2) = 7 and gcd(7, 30) = 1.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000 (first 1709 terms from Amiram Eldar)
• Index entries for sequences computed from exponents in factorization of n.

Crossrefs

Cf. A000005, A354178.

Subsequence of A350014.

Programs

Mathematica

Select[Range[25000], CoprimeQ[DivisorSigma[0, #^2], 30] &]

PARI

isok(m) = gcd(numdiv(m^2), 30) == 1; \\ Michel Marcus, May 19 2022

Formula

a(n) = sqrt(A354178(n)).

Sum_{n>=1} 1/a(n) = Product_{p prime} (p + p^4 + p^6 + p^7 + p^9 + p^10 + p^12 + p^15)/(p^15 - 1) = 1.2449394393...