A156833 A054525 * A156348 * [1,2,3,...].

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

Offset: 1

Author

Gary W. Adamson, Feb 16 2009

Keywords

• nonn

Comments

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

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

Examples

			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

Programs

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

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 *)

Formula

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

Extensions

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