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 A064727 Number of pairs x,y such that 0 < x <= y < n and x+y = n and x*y = kn for some k. 1
 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 3, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 4, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 2, 1, 0, 0, 0, 2, 4, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 3, 1, 5, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS a(n)=0 when n is a prime or a nonsquare semiprime. Other values of n so that a(n)=0 are 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, 170, 174, 182, 186, 190, 195, 210, 222, 230, 231. When n is a square, a(n) = floor(sqrt(n)/2) and is a record value in the sequence. [corrected by Jon E. Schoenfield, Nov 18 2017] Number of partitions of n into two parts (s,t) such that (s+t) | s*t. - Wesley Ivan Hurt, Apr 29 2021 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = Sum_{i=1..floor(n/2)} (1-ceiling(i*(n-i)/n)+floor(i*(n-i)/n). - Wesley Ivan Hurt, Apr 29 2021 EXAMPLE a(16) = 2 because 4+12 = 16 and 4*12 = 48 = 3*16, 8+8 = 16 and 8*8 = 4*16. MAPLE P:=proc(n) local a, k; a:=0; for k from 1 to trunc(n/2) do if frac(k*(n-k)/n)=0 then a:=a+1; fi; od; a; end: seq(P(i), i=1..105); # Paolo P. Lava, Jan 30 2018 MATHEMATICA Table[Count[IntegerPartitions[n, {2}], _?(Divisible[Apply[Times, #], n] &)], {n, 105}] (* Michael De Vlieger, Nov 18 2017 *) PROG (PARI) A064727(n) = { my(s=0); for(x=1, n, y = (n-x); if((x<=y)&&(0==((x*y)%n)), s++)); (s); }; \\ Antti Karttunen, Nov 18 2017 CROSSREFS Sequence in context: A158971 A121467 A071325 * A343222 A112378 A324832 Adjacent sequences:  A064724 A064725 A064726 * A064728 A064729 A064730 KEYWORD nonn,look AUTHOR Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 14 2001 EXTENSIONS Offset corrected (to 1) by Antti Karttunen, Nov 18 2017 STATUS approved

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Last modified September 18 09:05 EDT 2021. Contains 347518 sequences. (Running on oeis4.)