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A174688 All different products of not necessarily distinct terms of A001317. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 21:07 EST 2021. Contains 349344 sequences. (Running on oeis4.)