cp's OEIS Frontend

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

%I A138808 #31 Mar 14 2017 00:14:01
%S A138808 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 A138808 65,74,81,96,57,109,61,112,101,98,101,138,73,110,121,151,81,160,85,
%U A138808 160,161,134,93,196,133,185,161,192,105,216,173,223,181,170,117,258
%N A138808 Number of integer pairs (x,y), x > 0, y > 0, such that x <= p, y <= q for any factorization n = p*q.
%C A138808 Conjecture: the row sums of the plane partitions A010766 are upper bounds. - _R. J. Mathar_, Aug 06 2008
%C A138808 a(n) is divisible by n iff n=1 or n belongs to A227993. - _Rémy Sigrist_, Mar 06 2017
%C A138808 a(n) >= 2*n - 1, with equality iff n is not composite. - _Rémy Sigrist_, Mar 12 2017
%H A138808 Paul Tek, <a href="/A138808/b138808.txt">Table of n, a(n) for n = 1..10000</a>
%H A138808 Rémy Sigrist, <a href="/A138808/a138808.png">Illustration of the first terms</a>
%F A138808 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 A138808 a(8) = these 20 marked *'s:
%e A138808 -|12345678
%e A138808 -+--------
%e A138808 1|********
%e A138808 2|****
%e A138808 3|**
%e A138808 4|**
%e A138808 5|*
%e A138808 6|*
%e A138808 7|*
%e A138808 8|*
%o A138808 (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 A138808 Cf. A227993.
%K A138808 nonn
%O A138808 1,2
%A A138808 _Jonas Wallgren_, May 16 2008
%E A138808 More terms from _Paul Tek_, Mar 21 2015
%E A138808 Typo in name corrected by _Rémy Sigrist_, Mar 05 2017