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

1,2

Comments

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

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.

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...

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A354178.

Subsequence of A350014.

Sequence in context: A270421 A056729 A070265 * A262675 A102834 A370786

Adjacent sequences: A354176 A354177 A354178 * A354180 A354181 A354182

Keyword

nonn

Author

Amiram Eldar, May 18 2022

Status

approved