OFFSET
1,2
COMMENTS
All the terms are squares since their number of divisors is odd.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Titus Hilberdink, How often is d(n) a power of a given integer?, Journal of Number Theory, Vol. 236 (2022), pp. 261-279.
FORMULA
The number of terms <= x is c*sqrt(x) + O(x^(1/6)), where c = Product_{p prime} (1 - 1/p)*(Sum_{k in A003593} 1/p^((k-1)/2)) = 0.8747347138... (Hilberdink, 2022).
EXAMPLE
MATHEMATICA
p35Q[n_] := n == 3^IntegerExponent[n, 3] * 5^IntegerExponent[n, 5]; Select[Range[60]^2, p35Q[DivisorSigma[0, #]] &]
PROG
(PARI) is(n) = n==3^valuation(n, 3)*5^valuation(n, 5); \\ A003593
isok(m) = is(numdiv(m)); \\ Michel Marcus, May 19 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 18 2022
STATUS
approved