|
%I #17 Oct 29 2017 19:30:02
%S 1,2,4,6,8,10,13,16,19,22,25,28,32,36,40,44,48,52,56,60,64,68,72,76,
%T 81,86,91,96,101,106,111,116,121,126,131,136,141,146,151,156,161,166,
%U 171,176,181,186,191,196,202,208,214,220,226,232,238,244,250,256,262,268
%N a(1)=1. a(n+1) = a(n) + (number of terms, from among the first n terms of the sequence, which occur among (d(1),d(2),d(3),...d(n)), where d(n) = A000005(n)).
%C The first differences never decrease so a very concise sequence from which this sequence can be reconstituted is the number of terms whose first difference is k: 1, 4, 6, 12, 24, 72, 720, 120, 300, 36, 384, 840, 552, 1024, 944, 1680, 840, 2520, ... - _Robert G. Wilson v_
%H G. C. Greubel, <a href="/A130798/b130798.txt">Table of n, a(n) for n = 1..5000</a>
%e The terms among the first 12 terms of {a(k)} which occur among the first 12 values of sequence A000005 are a(1) = 1 (A000005(1)), a(2) = 2 (A000005(2)), a(3) = 4 (A000005(6)) and a(4) = 6 (A000005(12)). There are 4 such terms, so a(13) = a(12) + 4 = 32.
%p with(numtheory): a[1] := 1: for n from 2 to 60 do a[n] := a[n-1] + nops(`intersect`({seq(a[i], i = 1 .. n-1)}, {seq(tau(i), i = 1 .. n-1)})) end do: seq(a[n], n = 1 .. 60); # _Emeric Deutsch_, Jul 21 2007
%t f[l_] := Append[l, l[[ -1]] + Count[MemberQ[l, # ] & /@ Union@ DivisorSigma[0, Range@ Length@ l], True]]; Nest[f, {1}, 59] (* _Robert G. Wilson v_, Aug 26 2007 *)
%Y Cf. A000005. See A105434 for a variant.
%K nonn
%O 1,2
%A _Leroy Quet_, Jul 15 2007
%E More terms from _Joshua Zucker_ and _Emeric Deutsch_, Jul 18 2007
|
