A380265 a(n) is the denominator of the mean value of A051903(k) at the range k = 1..n.

1, 2, 3, 1, 1, 1, 1, 4, 3, 10, 11, 3, 13, 7, 15, 16, 17, 9, 19, 20, 7, 22, 23, 24, 25, 13, 27, 28, 29, 2, 31, 32, 33, 34, 35, 9, 37, 19, 39, 20, 41, 21, 43, 44, 15, 23, 47, 16, 7, 50, 51, 26, 53, 27, 55, 28, 57, 29, 59, 12, 61, 62, 7, 64, 65, 66, 67, 34, 23, 5, 71

Offset: 1

Author

Amiram Eldar, Jan 18 2025

Keywords

• nonn
• easy
• frac

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• 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.
• Wikipedia, Niven's constant.

Crossrefs

Cf. A051903, A380264 (numerators).

Programs

Mathematica

f[n_] := Max[FactorInteger[n][[;;, 2]]]; f[1] = 0; With[{m = 100}, Denominator[Accumulate[Array[f, m]] / Range[m]]]

PARI

lista(nmax) = {my(s = 0); print1(1, ", "); for(n = 2, nmax, s += vecmax(factor(n)[,2]);  print1(denominator(s/n), ", "));}

Formula

a(n) = denominator((Sum_{k=1..n} A051903(k))/n).