A143112 A051731 * A032742 = sum of largest proper divisors of the divisors of n.

1, 2, 2, 4, 2, 6, 2, 8, 5, 8, 2, 14, 2, 10, 8, 16, 2, 18, 2, 20, 10, 14, 2, 30, 7, 16, 14, 26, 2, 32, 2, 32, 14, 20, 10, 44, 2, 22, 16, 44, 2, 42, 2, 38, 26, 26, 2, 62, 9, 38, 20, 44, 2, 54, 14, 58, 22, 32, 2, 80, 2, 34, 34, 64, 16, 62, 2, 56, 26, 58, 2, 96, 2, 40, 38, 62, 14, 72, 2, 92

Offset: 1

Author

Gary W. Adamson and Mats Granvik, Jul 25 2008

Keywords

• nonn

Comments

Inverse Möbius transform of A032742. - Antti Karttunen, Sep 25 2018

Examples

			a(12) = 14. The divisors of 12 are shown in row 12 of triangle A127093: (1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12). The largest proper divisors of these terms are (1, 1, 1, 2, 0, 3, 0, 0, 0, 0, 0, 6), sum = 14. Or, we can take row of triangle A051731: (1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1) dot (1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6) = (1 + 1 + 1 + 2 + 0 + 3 + 0 + 0 + 0 + 0 + 0 + 6) = 14, where A032742 = (1, 1, 1, 2, 1, 3, 1, 4, 3, 5,...).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A051731, A127093, A032742, A300236, A305807, A305808.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A143112(n) = sumdiv(n,d,A032742(d)); \\ Antti Karttunen, Sep 25 2018

Formula

A051731 * A032742, where A051731 = the inverse Mobius transform and A032742 = the largest proper divisors of n: (1, 1, 1, 3, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7,...).

a(n) = Sum_{d|n} A032742(d). - Antti Karttunen, Sep 25 2018

Extensions

More terms from R. J. Mathar, Jan 19 2009