A130798 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)).

1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268

Offset

1,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

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.

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A000005. See A105434 for a variant.

Sequence in context: A129011 A130174 A061168 * A165453 A282168 A025224

Adjacent sequences: A130795 A130796 A130797 * A130799 A130800 A130801

Keyword

nonn

Author

Leroy Quet, Jul 15 2007

Extensions

More terms from Joshua Zucker and Emeric Deutsch, Jul 18 2007

Status

approved