A217895 Sum of d/Gpf(d) for all divisors d of n, with Gpf(d) the greatest prime factor of d.

1, 2, 2, 4, 2, 5, 2, 8, 5, 5, 2, 11, 2, 5, 6, 16, 2, 14, 2, 11, 6, 5, 2, 23, 7, 5, 14, 11, 2, 17, 2, 32, 6, 5, 8, 32, 2, 5, 6, 23, 2, 17, 2, 11, 18, 5, 2, 47, 9, 20, 6, 11, 2, 41, 8, 23, 6, 5, 2, 39, 2, 5, 18, 64, 8, 17, 2, 11, 6, 23, 2, 68, 2, 5, 26, 11, 10

Offset

1,2

Comments

a(n) <= n (see Proposition 5.2 in Girard's paper, link below).

a(p) = 2, when p is prime.

Links

Altug Alkan, Table of n, a(n) for n = 1..10000

Benjamin Girard, On a combinatorial problem of Erdos, Kleitman and Lemke, arXiv:1010.5042 [math.CO], 2010-2012.

Benjamin Girard, On a combinatorial problem of Erdos, Kleitman and Lemke, Advances in Mathematics 231, 3-4 (2012) 1843-1857.

Example

The divisors of 6 are : 1, 2, 3, 6; so a(6)=1/gpf(1)+2/gpf(2)+3/gpf(3)+6/gpf(6) = 1/1 + 2/2 + 3/3 + 6/3 = 5.

Mathematica

a[n_] := Sum[d/FactorInteger[d][[-1, 1]], {d, Divisors[n]}];
Array[a, 80] (* Jean-François Alcover, Sep 26 2018 *)

Prog

(PARI) gpf(n) = {if (n==1, return (1), return (vecmax(factor(n)[, 1]))); }
a(n)= { my(d = divisors(n)); sum(j=1, length(d), d[j]/gpf(d[j])); } \\ revised by Michel Marcus, Sep 26 2018

Crossrefs

Cf. A052126 (Mobius transform).

Sequence in context: A304442 A057567 A353845 * A328720 A005128 A187782

Adjacent sequences: A217892 A217893 A217894 * A217896 A217897 A217898

Keyword

nonn

Author

Michel Marcus, Oct 14 2012

Status

approved