OFFSET
1,1
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..5000
EXAMPLE
k=24, x=8, y=16 and 24=8+16; k'=44, x'=12, y'=32 and 44=12+32.
In more than one way:
k=39, x=4, y=35 and 39=4+35; k'=16, x'=4, y'=12 and 16=4+12;
k=39, x=13, y=26 and 39=13+26; k'=16, x’=1, y'=15 and 16=1+15.
k=255, x=54, y=201 and 255=54+201; k'=151, x'=81, y'=70 and 16=4+12;
k=255, x=85, y=170 and 255=85+170; k'=151, x'=22, y'=129 and 16=1+15;
k=255, x=114, y=141 and 39=13+26; k'=151, x'=101, y'=50 and 16=1+15.
MAPLE
with(numtheory);
A212662:=proc(q)
local a, b, c, i, n, p, pfs;
for n from 1 to q do
pfs:=ifactors(n)[2]; a:=n*add(op(2, p)/op(1, p), p=pfs);
for i from 1 to trunc(n/2) do
pfs:=ifactors(i)[2]; b:=i*add(op(2, p)/op(1, p), p=pfs);
pfs:=ifactors(n-i)[2]; c:=(n-i)*add(op(2, p)/op(1, p), p=pfs);
if a=b+c then print(n); break; fi;
od;
od; end:
A212662(1000);
PROG
(PARI) ard(n)=vecsum([n/f[1]*f[2]|f<-factor(n+!n)~]); \\ A003415
isok(m) = for (k=1, m\2, if (ard(m-k)+ard(k) == ard(m), return(1))); \\ Michel Marcus, Aug 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 23 2012
STATUS
approved