A138808 Number of integer pairs (x,y), x > 0, y > 0, such that x <= p, y <= q for any factorization n = p*q.

1, 3, 5, 8, 9, 14, 13, 20, 21, 26, 21, 35, 25, 38, 41, 48, 33, 57, 37, 64, 61, 62, 45, 84, 65, 74, 81, 96, 57, 109, 61, 112, 101, 98, 101, 138, 73, 110, 121, 151, 81, 160, 85, 160, 161, 134, 93, 196, 133, 185, 161, 192, 105, 216, 173, 223, 181, 170, 117, 258

Offset

1,2

Comments

Conjecture: the row sums of the plane partitions A010766 are upper bounds. - R. J. Mathar, Aug 06 2008

a(n) is divisible by n iff n=1 or n belongs to A227993. - Rémy Sigrist, Mar 06 2017

a(n) >= 2*n - 1, with equality iff n is not composite. - Rémy Sigrist, Mar 12 2017

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of the first terms

Formula

a(n) = n*(m - Sum_{k=1..m-1} d(k)/d(k+1)), where d(1) < d(2) < ... < d(m) denote the divisors of n. - Rémy Sigrist, Mar 06 2017

Example

a(8) = these 20 marked *'s:
-|12345678
-+--------
1|********
2|****
3|**
4|**
5|*
6|*
7|*
8|*

Prog

(PARI) a(n) = my(ar=0, pw=0); fordiv(n, w, ar=ar+(w-pw)*n/w; pw=w); return (ar) \\ Paul Tek, Mar 21 2015

Crossrefs

Cf. A227993.

Sequence in context: A002159 A050094 A137319 * A185456 A308405 A331314

Adjacent sequences: A138805 A138806 A138807 * A138809 A138810 A138811

Keyword

nonn

Author

Jonas Wallgren, May 16 2008

Extensions

More terms from Paul Tek, Mar 21 2015

Typo in name corrected by Rémy Sigrist, Mar 05 2017

Status

approved