A174688 All different products of not necessarily distinct terms of A001317.

1, 3, 5, 9, 15, 17, 25, 27, 45, 51, 75, 81, 85, 125, 135, 153, 225, 243, 255, 257, 289, 375, 405, 425, 459, 625, 675, 729, 765, 771, 867, 1125, 1215, 1275, 1285, 1377, 1445, 1875, 2025, 2125, 2187, 2295, 2313, 2601, 3125, 3375, 3645, 3825, 3855, 4131, 4335, 4369

Offset

1,2

Comments

Sequence differs from A143512 beginning with a(970).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = 2.

Let m_a(n) = (-1)^A010060(n), if n is squarefree, and 0, otherwise (a-analog of Möbius function). Then Sum_{n>=1} m_a(n)/a(n) = 1/2.

A generalization: Sum_{n>=1} 1/(a(n))^s = Product_{Fermat numbers F} (1-F^(-s))^(-1), where s>0 (an analog of Euler identity for primes, where, for real s, s>1).

Example

9 = 3^2 is a term since 3 is in A001317.

Mathematica

f[n_] := FromDigits[Table[Mod[Binomial[n, k], 2], {k, 0, n}], 2]; n = 13; v = Array[f, n, 0]; vmax = v[[-1]]; s = {1}; Do[v1 = v[[k]]; rmax = Floor[Log[v1, vmax]]; s1 = v1^Range[0, rmax]; s2 = Select[Union[Flatten[Outer[Times, s, s1]]], # <= vmax &]; s = Union[s, s2], {k, 2, n}]; s (* Amiram Eldar, Sep 27 2020 *)

Crossrefs

Cf. A001317, A000215, A143512.

Sequence in context: A209837 A093688 A143512 * A339345 A111249 A190804

Adjacent sequences: A174685 A174686 A174687 * A174689 A174690 A174691

Keyword

nonn

Author

Vladimir Shevelev, Dec 01 2010

Extensions

Offset corrected and more terms added by Amiram Eldar, Sep 27 2020

Status

approved