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A144366 Shifts 2 places left under Dirichlet convolution. 3
1, 1, 1, 2, 2, 5, 4, 12, 8, 28, 17, 60, 34, 134, 68, 276, 140, 580, 280, 1186, 560, 2436, 1128, 4906, 2256, 9976, 4516, 20020, 9048, 40324, 18096, 80860, 36192, 162320, 72418, 324920, 144852, 651177, 289704, 1302914, 579476, 2608360, 1158952 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

FORMULA

G.f.: x + x^2 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - Ilya Gutkovskiy, May 09 2019

MAPLE

k:= 2: with(numtheory): dck:= proc(b, c) proc(n, k) option remember; add(b(d, k) *c(n/d, k), d=`if`(n<0, {}, divisors(n))) end end: B:= dck(T, T): T:= (n, k)-> if n<=k then 1 else B(n-k, k) fi: a:= n-> T(n, k): seq(a(n), n=1..50);

MATHEMATICA

k = 2; dck[b_, c_][n_, k_] := dck[b, c][n, k] = DivisorSum[n, b[#, k] * c[n/#, k]&]; B = dck[T, T]; T[n_, k_] :=  If[n <= k, 1, B[n-k, k]]; a[n_] := T[n, k]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Apr 05 2017, translated from Maple *)

CROSSREFS

2nd column of A144374. Cf. A000005.

Sequence in context: A124506 A264687 A112471 * A054156 A238834 A284686

Adjacent sequences:  A144363 A144364 A144365 * A144367 A144368 A144369

KEYWORD

eigen,nonn

AUTHOR

Alois P. Heinz, Sep 18 2008

STATUS

approved

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Last modified April 17 08:34 EDT 2021. Contains 343064 sequences. (Running on oeis4.)