A187807 Numbers n that can be expressed as the sum of the arithmetic derivatives of k previous numbers starting from n for some k >= 1.

4, 5, 6, 7, 27, 42, 43, 1310, 3125, 47058, 47059, 151747, 192382, 192383, 244419, 257614, 823543, 28170538, 28170539, 36861843, 48647587, 556429758, 2736456639, 26781610526

Offset

1,1

Comments

A051674 is a subsequence of this sequence.

Links

Table of n, a(n) for n=1..24.

Formula

n = Sum{j=1..k} (n-j+1)', for some k >= 1.

Example

k=1: n=27 -> 27 = 27'.
k=2: n=1310 -> 1310 = 1310'+1309' = 927+383.
k=3: n=43 -> 43 = 43'+42'+41' = 1+41+1.

Maple

with(numtheory);
A187807:= proc(i)
local a, b, c, n.p;
for n from 4 to i do
  a:=0; b:=-1;
  while a<n do b:=b+1; a:=a+(n-b)*add(op(2, p)/op(1, p), p=ifactors(n-b)[2]); od;
  if a=n then print(n); fi; od; end:
A187807(100000000);

Crossrefs

Cf. A003415, A051674, A195333, A216384.

Sequence in context: A030677 A071177 A010754 * A051036 A063673 A105737

Adjacent sequences: A187804 A187805 A187806 * A187808 A187809 A187810

Keyword

nonn,more

Author

Paolo P. Lava, Jan 07 2013

Extensions

a(22)-a(24) from Donovan Johnson, Jan 26 2013

Status

approved