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

1,2

Comments

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

Links

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

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

Example

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,...).

Prog

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

Crossrefs

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

Sequence in context: A137502 A318885 A307088 * A286472 A279690 A167272

Adjacent sequences: A143109 A143110 A143111 * A143113 A143114 A143115

Keyword

nonn

Author

Gary W. Adamson and Mats Granvik, Jul 25 2008

Extensions

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

Status

approved