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A354179
Numbers whose square has a number of divisors that is coprime to 30.
3
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).
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
Subsequence of A350014.
Sequence in context: A270421 A056729 A070265 * A262675 A102834 A376171
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 18 2022
STATUS
approved