The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A156833

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A156833

A054525 * A156348 * [1,2,3,...]
(history; published version)

#9 by Joerg Arndt at Sun Oct 15 11:20:11 EDT 2023

STATUS

reviewed

approved

#8 by Michel Marcus at Sun Oct 15 11:01:03 EDT 2023

STATUS

proposed

reviewed

#7 by Jean-François Alcover at Sun Oct 15 08:49:40 EDT 2023

STATUS

editing

proposed

#6 by Jean-François Alcover at Sun Oct 15 08:49:28 EDT 2023

MATHEMATICA

A054525[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0];

A156348[n_, k_] := Which[k < 1 || k > n, 0, Mod[n, k] == 0, Binomial[n/k - 2 + k, k - 1], True, 0];

T[n_, k_] := Sum[A054525[n, j]*A156348[j, k], {j, k, n}];

a[n_] := Sum[T[n, k]*k, {k, 1, n}];

Table[a[n], {n, 1, 51}] (* Jean-François Alcover, Oct 15 2023 *)

STATUS

approved

editing

#5 by Joerg Arndt at Sun Mar 03 13:48:57 EST 2013

STATUS

proposed

approved

#4 by R. J. Mathar at Sun Mar 03 12:41:26 EST 2013

STATUS

editing

proposed

#3 by R. J. Mathar at Sun Mar 03 12:41:08 EST 2013

DATA

1, 2, 3, 6, 5, 16, 7, 24, 24, 38, 11, 103, 13, 68, 127, 144, 17, 261, 19, 404, 291, 152, 23, 994, 370, 206, 540, 1093, 29, 2195, 31, 1584, 943, 338, 2543, 4808, 37, 416, 1479, 7371, 41, 7929, 43, 4691, 8976, 596, 47, 18876, 6510, 11035, 3091

MAPLE

A156833T := proc(n, k)

add(A054525(n, j)*A156348(j, k), j=k..n) ;

end proc:

A156833 := proc(n)

add(A156833T(n, k)*k, k=1..n) ;

end proc: # R. J. Mathar, Mar 03 2013

EXTENSIONS

Extended beyond a(14) by R. J. Mathar, Mar 03 2013

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 17:25:34 EDT 2012

AUTHOR

_Gary W. Adamson (qntmpkt(AT)yahoo.com), _, Feb 16 2009

Discussion

Fri Mar 30

17:25

OEIS Server: https://oeis.org/edit/global/135

#1 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

A054525 * A156348 * [1,2,3,...]

DATA

1, 2, 3, 6, 5, 16, 7, 24, 24, 38, 11, 103, 13, 68

OFFSET

1,2

COMMENTS

Conjecture: for n>1, a(n) = n iff n is prime.

Companion to A156834: (1, 2, 3, 5, 5, 12, 7, 17, 19,...).

FORMULA

A054525 * A156348 * [1,2,3,...]

EXAMPLE

a(4) = 6 since first 4 terms of A156348 * [1, 2, 3, 4,...] = (1, 3, 4, 9);

Then (1, 3, 4, 9) dot (0, -1, 0, 1) = (0 - 3 + 0 + 9) = 6. Row 4 of A054525 = (0, -1, 0, 1).

CROSSREFS

Cf. A156348, A054525, A156834

KEYWORD

nonn,new

AUTHOR

Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 16 2009

STATUS

approved