A380266 -id:A380266 - cp's OEIS frontend

A086195 Incorrect version of A380266.

1, 2, 3, 1, 1, 1, 1, 11, 13, 14, 5, 16, 17, 6, 19, 23, 4, 25, 13, 9, 14, 29, 5, 31, 33, 34, 37, 38, 13, 40, 41, 46, 47, 48, 49, 51, 26, 53, 27, 55, 4, 57, 29, 59, 30, 61, 31, 9, 13, 22, 67, 68, 23, 14, 71, 24, 73, 74, 5, 76, 77, 26, 79, 17, 43, 87, 22, 89, 9, 91, 23, 94, 95

Offset: 1

Eric W. Weisstein, Jul 11 2003

Previous name was: Numerators of running averages of A051904.

Due to a bug in the Mathematica code in the World of Mathematics page, the sequence was calculated with running averages over {A051904(1), 1, A051904(2), A051904(3), ... } with the first term removed. See A380266 for the correct sequence. - Amiram Eldar, Jan 18 2025

			1/2, 2/3, 3/4, 1, 1, 1, 1, 11/9, 13/10, 14/11, ...

Eric Weisstein's World of Mathematics, Niven's Constant.

Cf. A051904, A086196 (denominators), A380266.

f[n_] := Min[FactorInteger[n][[;; , 2]]]; f[1] = 0; With[{m = 100}, Numerator[(1 + Accumulate[Array[f, m]]) / Range[2, m + 1]]] (* Amiram Eldar, Jan 18 2025 *)

a(n) = numerator((1 + Sum_{k=1..n} A051904(k))/(n+1)). - Amiram Eldar, Jan 18 2025

A380267 a(n) is the denominator of the mean value of A051904(k) at the range k = 1..n.

Original entry on oeis.org

1, 2, 3, 1, 1, 1, 1, 4, 3, 10, 11, 4, 13, 14, 5, 8, 17, 3, 19, 10, 7, 11, 23, 4, 25, 26, 3, 28, 29, 10, 31, 32, 33, 34, 35, 18, 37, 19, 39, 20, 41, 3, 43, 22, 45, 23, 47, 24, 49, 10, 17, 52, 53, 18, 11, 56, 19, 58, 59, 4, 61, 62, 21, 16, 13, 33, 67, 17, 69, 7

Offset: 1

Amiram Eldar, Jan 18 2025

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.

Cf. A051904, A380266 (numerators).

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

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

a(n) = denominator((Sum_{k=1..n} A051904(k))/n).

cp's OEIS Frontend

A086195 Incorrect version of A380266.

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