A158907 Row sums of triangle A158906.

1, 3, 4, 6, 6, 9, 8, 11, 11, 13, 12, 17, 14, 17, 18, 20, 18, 23, 20, 25, 24, 25, 24, 31, 27, 29, 30, 33, 30, 37, 32, 37, 36, 37, 38, 44, 38, 41, 42, 47, 42, 49, 44, 49, 50, 49, 48, 57, 51, 55, 54, 57, 54, 61, 58, 63, 60, 61, 60

Offset

1,2

Comments

This is the number of pairs of positive integers (i,j) such that i*j = n or i+j = n (where (2,2) is double-counted as both 2+2=4 and 2*2=4.) - Peter Kagey, Oct 02 2020

Links

Table of n, a(n) for n=1..59.

Formula

a(n) = Sum_{k=1..n} A158906(n,k).

a(p) = p + 1 for prime p. [corrected by Ruediger Jehn, Dec 25 2020]

a(n) = A032741(n) + n. - R. J. Mathar, Jan 08 2015

a(n) = Sum_{i=1..n} floor(n/i)-floor((n-1)/(i+1)). - Wesley Ivan Hurt, Sep 13 2017

Example

a(4) = 6 = (4 + 1 + 0 + 1).

Maple

A158906 := proc(n, k)
    add( A158821(n-1, j-1)*A051731(j, k), j=k..n) ;
end proc:
A158907 := proc(n)
    add(A158906(n, k), k=1..n) ;
end proc:
seq(A158907(n), n=1..62) ; # R. J. Mathar, Jan 08 2015

Crossrefs

Cf. A032741, A158906.

Sequence in context: A284061 A162625 A033095 * A338281 A338723 A175708

Adjacent sequences: A158904 A158905 A158906 * A158908 A158909 A158910

Keyword

nonn,easy

Author

Gary W. Adamson and Mats Granvik, Mar 29 2009

Status

approved