A292362 Least numbers k that can be expressed as k = a' + b', with k = a + b, in exactly n ways, where a' and b' are the arithmetic derivatives of a and b.

1, 0, 27, 999, 573, 14121, 27675, 68600, 3528, 192672, 121000, 158184

Offset

0,3

Comments

a(n) > 5*10^6 for n > 11. - Giovanni Resta, Sep 26 2017

Links

Table of n, a(n) for n=0..11.

Example

a(0) = 1.
a(1) = 0 = 0' + 0'.
a(2) = 27 = 0' + 27' = 9' + 18'.
a(3) = 999 = 33' + 966' =  234' + 765' = 306' + 693'.
a(4) = 573 = 89' + 484' = 97' + 476' = 113' + 460' = 197' + 376'.
a(5) = 14121 = 5' + 14116' = 2391' + 11730' = 5310' + 8811' = 6039' + 8082' = 6066' + 8055'.
a(6) = 27675 = 2304' + 25371' = 7110' + 20565' = 8304' + 19371' = 8520' + 19155' = 11220' + 16455' = 12639' + 15036'.

Maple

with(numtheory): P:=proc(q) local a, b, c, k, n, p, x; x:=array(1..50);
for n from 1 to 50 do x[n]:=0; od; x[1]:=1; lprint(0, 1); lprint(1, 0);
for n from 1 to q do c:=0; for k from 0 to trunc(n/2) do
a:=k*add(op(2, p)/op(1, p), p=ifactors(k)[2]);
b:=(n-k)*add(op(2, p)/op(1, p), p=ifactors(n-k)[2]);
if a+b=n then c:=c+1; fi; od; if c>0 then if x[c]=0 then
x[c]:=n; lprint(c, x[c]); fi; fi; od;  end: P(10^9);
# program presents a(n) not in order but as they first appear

Crossrefs

Cf. A003415.

Sequence in context: A107050 A129999 A132059 * A239571 A017019 A143366

Adjacent sequences: A292359 A292360 A292361 * A292363 A292364 A292365

Keyword

nonn,hard,more

Author

Paolo P. Lava, Sep 15 2017

Extensions

a(7), a(9)-a(11) by Giovanni Resta, Sep 26 2017

Status

approved