A213241 Numbers n for which n=(n'' mod n'), where n' and n'' are the first and second arithmetic derivative of n.

16, 20, 64, 108, 135, 164, 352, 432, 729, 1024, 1107, 2376, 2916, 6912, 12500, 15625, 16038, 16384, 19683, 43692, 46656, 47616, 50000, 84375, 110592, 128125, 188228, 275000, 294921, 314928, 321408, 337500, 746496, 800000, 1270539, 1856250

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

n=432, n'=1296, n''=4320 and 4320=1296*3+432.

Maple

with(numtheory);
A213241:= proc(i)
local a, b, n, p, pfs;
for n from 1 to i do
  pfs:=ifactors(n)[2]; a:=n*add(op(2, p)/op(1, p), p=pfs);
  pfs:=ifactors(a)[2]; b:=a*add(op(2, p)/op(1, p), p=pfs);
  pfs:=ifactors(b)[2]; c:=b*add(op(2, p)/op(1, p), p=pfs);
  if a>0 then if (b mod a)=n then print(n); fi; fi;
od;
end:
A213241(10000000);

Crossrefs

Cf. A003415

Sequence in context: A104010 A102544 A152022 * A219395 A260572 A240038

Adjacent sequences: A213238 A213239 A213240 * A213242 A213243 A213244

Keyword

nonn

Author

Paolo P. Lava, Jun 12 2012

Status

approved