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#11 by Peter Luschny at Mon Jul 08 06:55:05 EDT 2019
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#10 by Jean-François Alcover at Mon Jul 08 06:25:53 EDT 2019
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#9 by Jean-François Alcover at Mon Jul 08 06:25:48 EDT 2019
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| MATHEMATICA
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A205957[n_] := Exp[-Sum[MoebiusMu[p] Log[k/p], {k, 1, n}, {p, FactorInteger[k][[All, 1]]}]];
Table[A205957[n], {n, 0, 30}] // DeleteDuplicates (* Jean-François Alcover, Jul 08 2019 *)
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| STATUS
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approved
editing
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#8 by T. D. Noe at Thu Sep 06 20:14:39 EDT 2012
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#7 by Peter Luschny at Mon Sep 03 09:26:23 EDT 2012
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#6 by Peter Luschny at Mon Sep 03 09:26:19 EDT 2012
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#5 by Peter Luschny at Mon Sep 03 09:24:08 EDT 2012
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#4 by Peter Luschny at Mon Sep 03 09:17:45 EDT 2012
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| COMMENTS
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The distinct values of A205957. Partial products of A216153.
Partial products of A216153.
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| LINKS
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Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/VonMangoldtTransformation">The von Mangoldt Transformation.</a>
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#3 by Peter Luschny at Sun Sep 02 15:12:23 EDT 2012
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| NAME
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allocatedA205957(n) where n is fora Peternonprime Luschnynumber.
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| DATA
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1, 2, 12, 48, 144, 1440, 34560, 483840, 7257600, 58060800, 3135283200, 125411328000, 2633637888000, 57940033536000, 5562243219456000, 27811216097280000, 723091618529280000, 6507824566763520000, 364438175738757120000, 327994358164881408000000
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| OFFSET
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1,2
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| COMMENTS
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The distinct values of A205957.
Partial products of A216153.
a(1),...,a(10) are highly totient numbers (A097942) and products of distinct factorials (A058295). The author conjectures that this is true in general.
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| LINKS
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Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/VonMangoldtTransformation">The von Mangoldt Transformation.</a>
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| FORMULA
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a(n) = A205957(A0182521(n)).
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| PROG
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(Sage)
# sorted(list(set([A205957(n) for n in (0..31)])))
def A216152_list(n) :
C = filter(lambda k: not is_prime(k), (1..n))
return [A205957(c) for c in C]
A216152_list(31)
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| CROSSREFS
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Cf. A051451.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Peter Luschny, Sep 02 2012
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| STATUS
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approved
editing
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Discussion
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| Mon Sep 03
| 03:42
| Joerg Arndt: I approved one (or two?) sequences that were still in the edit-queue, please reopen if necessary!
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#2 by Peter Luschny at Sun Sep 02 11:51:11 EDT 2012
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| KEYWORD
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allocating
allocated
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