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A138808
Number of integer pairs (x,y), x > 0, y > 0, such that x <= p, y <= q for any factorization n = p*q.
2
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
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
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