

A273227


Consider all ways of writing the nth composite number as the product of two divisors d1*d2 = d3*d4 = ...; a(n) is the minimum of the sums {d1 + d2, d3 + d4, ...}.


3



4, 5, 6, 6, 7, 7, 9, 8, 8, 9, 9, 10, 13, 10, 10, 15, 12, 11, 11, 12, 14, 19, 12, 12, 21, 16, 13, 13, 15, 14, 25, 14, 14, 15, 20, 17, 15, 16, 15, 22, 31, 16, 33, 16, 16, 18, 17, 21, 26, 17, 17, 39, 20, 23, 18, 19, 18, 18, 43, 19, 22, 45, 32, 19, 19, 20, 27, 34
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OFFSET

1,1


COMMENTS

a(n) = A046343(n) if n is semiprime.
This sequence is included in A063655.  Giovanni Resta, May 18 2016
a(n) >= 2 * sqrt(A002808(n)).  David A. Corneth, May 20 2016


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

a(14) = 10 because A002808(14) = 24 = 2*12 = 3*8 = 4*6 and 4+6 = 10 is the minimum 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 n01 do:
p:=d[i]:
for j from i to n01 do:
q:=d[j]:
if p*q=n then
lst:=lst union {p+q}:
else
fi:
od:
od:
printf(`%d, `, lst[1]):
fi:
od:


MATHEMATICA

Function[n, If[OddQ@ Length@ #, 2 Sqrt@ n, Total@ Take[#, {Length[#]/2, Length[#]/2 + 1}]] &@ Divisors@ n] /@ Select[Range@ 93, CompositeQ] (* Michael De Vlieger, May 20 2016 *)
msd[n_]:=Module[{d=Divisors[n], len}, len=Length[d]; If[OddQ[len], 2*d[[ (len+1)/2]], d[[len/2]]+d[[len/2+1]]]]; msd/@Select[Range[200], CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 09 2018 *)


PROG

(PARI) forcomposite(n=4, 100, d=divisors(n); t=#d; k=if(t%2, 2*d[t\2+1], d[t\2]+d[t\2+1]); print1(k", ")) \\ Charles R Greathouse IV, Jun 08 2016


CROSSREFS

Cf. A002808, A046343, A063655.
Sequence in context: A058979 A225491 A046343 * A319500 A022911 A162310
Adjacent sequences: A273224 A273225 A273226 * A273228 A273229 A273230


KEYWORD

nonn


AUTHOR

Michel Lagneau, May 18 2016


EXTENSIONS

Name edited by Jon E. Schoenfield, Sep 12 2017


STATUS

approved



