login
A273777
Consider all ways of writing the n-th composite number as the product of two divisors d1*d2 = d3*d4 = ... where each divisor is larger than 1; a(n) is the maximum of the sums {d1 + d2, d3 + d4, ...}.
0
4, 5, 6, 6, 7, 8, 9, 8, 10, 11, 12, 10, 13, 14, 10, 15, 12, 16, 17, 18, 14, 19, 12, 20, 21, 16, 22, 23, 24, 18, 25, 26, 14, 27, 20, 28, 29, 16, 30, 22, 31, 32, 33, 24, 34, 18, 35, 36, 26, 37, 38, 39, 28, 40, 18, 41, 42, 30, 43, 44, 22, 45, 32, 46, 47, 20, 48
OFFSET
1,1
COMMENTS
The divisors must be > 1 and < n.
For the minimum sums see A273227.
FORMULA
Let m = A002808(n). Then a(n) = A020639(m) + m / A020639(m).
EXAMPLE
a(14) = 14 because A002808(14) = 24 = 2*12 = 3*8 = 4*6 and 2+12 = 14 is the maximum sum.
MAPLE
with(numtheory):nn:=100:lst:={}:
for n from 1 to nn do:
it:=0:lst:={}:
d:=divisors(n):n0:=nops(d):
if n0>2 then
for i from 2 to n0-1 do:
p:=d[i]:
for j from i to n0-1 do:
q:=d[j]:
if p*q=n then
lst:=lst union {p+q}:
else
fi:
od:
od:
n0:=nops(lst):printf(`%d, `, lst[n0]):
fi:
od:
MATHEMATICA
Function[n, Max@ Map[Plus[#, n/#] &, Rest@ Take[#, Ceiling[Length[#]/2]]] &@ Divisors@ n] /@ Select[Range@ 120, CompositeQ] (* Michael De Vlieger, May 30 2016 *)
PROG
(PARI) lista(nn) = {forcomposite(n=2, nn, m = 0; fordiv(n, d, if ((d != 1) && (d != n), m = max(m, d+n/d)); ); print1(m, ", "); ); } \\ Michel Marcus, Sep 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, May 30 2016
EXTENSIONS
Name edited by Jon E. Schoenfield, Sep 12 2017
STATUS
approved