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 A051904 Minimal exponent in prime factorization of n. 40
 0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The asymptotic mean of this sequence is 1 (Niven, 1969). - Amiram Eldar, Jul 10 2020 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 a(n) = min_{k=1..A001221(n)} A124010(n,k). - Reinhard Zumkeller, Aug 27 2011 a(1) = 0, for n > 1, if A001221(n) = 1 (when n is in A000961), a(n) = A001222(n), otherwise a(n) = min(A067029(n), a(A028234(n))). - Antti Karttunen, Jul 12 2017 EXAMPLE For n = 72 = 2^3*3^2, a(72) = min(exponents) = min(3,2) = 2. 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 Cf. A000961, A001221, A005361, A008479, A051903, A052409, A076558, A124010. Sequence in context: A158378 A052409 A327503 * A070012 A071178 A326515 Adjacent sequences:  A051901 A051902 A051903 * A051905 A051906 A051907 KEYWORD nonn,easy AUTHOR Labos Elemer, Dec 16 1999 STATUS approved

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Last modified July 3 17:50 EDT 2022. Contains 355055 sequences. (Running on oeis4.)