OFFSET
1,108
COMMENTS
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Horst Alzer and Man Kam Kwong, On Sándor's Inequality for the Riemann Zeta Function, J. Int. Seq. (2023) Vol. 26, Article 23.3.6.
FORMULA
a(n) << sqrt(log n)/log log n. - Charles R Greathouse IV, Sep 14 2015
From Antti Karttunen, Aug 18 2016: (Start)
These formulas use Iverson bracket, which gives 1 as its value if the condition given inside [ ] is true and 0 otherwise:
(End)
a(n) = Sum_{d|n} [rad(d) = Omega(d)*[omega(d) = 1]], where [ ] is the Iverson bracket. - Wesley Ivan Hurt, Feb 09 2022
Additive with a(p^e) = 1 if e >= p, and 0 otherwise. - Amiram Eldar, Nov 07 2022
EXAMPLE
Since 15 = 3^1 * 5^1, a(15) = 0. But 16 = 2^4 is divisible by 2^2, so a(16) = 1. - Michael B. Porter, Aug 18 2016
MATHEMATICA
{0}~Join~Table[Count[FactorInteger[n][[All, 1]], _?(Mod[n, #^#] == 0 &)], {n, 2, 120}] (* Michael De Vlieger, Oct 30 2019 *)
PROG
(PARI) a(n)=my(s, t, v); forprime(p=2, , v=valuation(n, p); if(v, n/=p^v; if(v>=p, s++), if(p^p>n, return(s)))) \\ Charles R Greathouse IV, Sep 14 2015
(Scheme, two variants)
(define (A129251 n) (if (= 1 n) 0 (+ (A129251 (A028234 n)) (if (zero? (modulo n (expt (A020639 n) (A020639 n)))) 1 0))))
;; Antti Karttunen, Aug 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Apr 07 2007
EXTENSIONS
Data section filled up to 120 terms by Antti Karttunen, Aug 18 2016
STATUS
approved