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URL: https://oeis.org/A212662

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A212662
Numbers k for which k' = x' + y', where x > 0, k = x + y, and k', x', y' are the arithmetic derivatives of k, x, y.
6
3, 6, 9, 12, 15, 18, 21, 24, 25, 27, 30, 33, 36, 39, 42, 45, 48, 50, 51, 54, 55, 57, 60, 63, 66, 69, 72, 75, 78, 81, 82, 84, 85, 87, 90, 93, 95, 96, 99, 100, 102, 105, 108, 110, 111, 114, 116, 117, 120, 121, 123, 125, 126, 129, 132, 135, 138, 141, 144, 145
OFFSET
1,1
LINKS
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