A138808 - OEIS

%I #31 Mar 14 2017 00:14:01

%S 1,3,5,8,9,14,13,20,21,26,21,35,25,38,41,48,33,57,37,64,61,62,45,84,

%T 65,74,81,96,57,109,61,112,101,98,101,138,73,110,121,151,81,160,85,

%U 160,161,134,93,196,133,185,161,192,105,216,173,223,181,170,117,258

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

%C Conjecture: the row sums of the plane partitions A010766 are upper bounds. - _R. J. Mathar_, Aug 06 2008

%C a(n) is divisible by n iff n=1 or n belongs to A227993. - _Rémy Sigrist_, Mar 06 2017

%C a(n) >= 2*n - 1, with equality iff n is not composite. - _Rémy Sigrist_, Mar 12 2017

%H Paul Tek, <a href="/A138808/b138808.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A138808/a138808.png">Illustration of the first terms</a>

%F 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

%e a(8) = these 20 marked *'s:

%e -|12345678

%e -+--------

%e 1|********

%e 2|****

%e 3|**

%e 4|**

%e 5|*

%e 6|*

%e 7|*

%e 8|*

%o (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

%Y Cf. A227993.

%K nonn

%O 1,2

%A _Jonas Wallgren_, May 16 2008

%E More terms from _Paul Tek_, Mar 21 2015

%E Typo in name corrected by _Rémy Sigrist_, Mar 05 2017