OFFSET
1,4
COMMENTS
The asymptotic mean of this sequence is 1 (Niven, 1969). - Amiram Eldar, Jul 10 2020
Let k = A007947(n), then for n > 1 k^a(n) is the greatest power of k which divides n; see example. - David James Sycamore, Sep 07 2023
LINKS
Daniel Forgues, Table of n, a(n) for n = 1..100000
Cao Hui-Zhong, The Asymptotic Formulas Related to Exponents in Factoring Integers, Math. Balkanica, Vol. 5 (1991), Fasc. 2.
Ivan Niven, Averages of Exponents in Factoring Integers, Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.
Eric Weisstein's World of Mathematics, Niven's Constant
FORMULA
EXAMPLE
For n = 72 = 2^3*3^2, a(72) = min(exponents) = min(3,2) = 2.
For n = 72, using alternative definition: rad(72) = 6; and 6^2 = 36 divides 72 but no higher power of 6 divides 72, so a(72) = 2.
For n = 432, rad(432) = 6 and 6^3 = 216 divides 432 but no higher power of 6 divides 432, therefore a(432) = 3. - David James Sycamore, Sep 08 2023
MAPLE
a := proc (n) if n = 1 then 0 else min(seq(op(2, op(j, op(2, ifactors(n)))), j = 1 .. nops(op(2, ifactors(n))))) end if end proc: seq(a(n), n = 1 .. 100); # Emeric Deutsch, May 20 2015
MATHEMATICA
Table[If[n == 1, 0, Min @@ Last /@ FactorInteger[n]], {n, 100}] (* Ray Chandler, Jan 24 2006 *)
PROG
(Haskell)
a051904 1 = 0
a051904 n = minimum $ a124010_row n -- Reinhard Zumkeller, Jul 15 2012
(PARI) a(n)=vecmin(factor(n)[, 2]) \\ Charles R Greathouse IV, Nov 19 2012
(Scheme) (define (A051904 n) (cond ((= 1 n) 0) ((= 1 (A001221 n)) (A001222 n)) (else (min (A067029 n) (A051904 (A028234 n)))))) ;; Antti Karttunen, Jul 12 2017
(Python)
from sympy import factorint
def a(n):
f = factorint(n)
l = [f[p] for p in f]
return 0 if n == 1 else min(l)
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Jul 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Dec 16 1999
STATUS
approved