The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A344599 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A344599

a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^3 - floor((n-1)/k)^3).
(history; published version)

#13 by Susanna Cuyler at Mon May 24 11:54:02 EDT 2021

STATUS

proposed

approved

#12 by Amiram Eldar at Mon May 24 09:28:13 EDT 2021

STATUS

editing

proposed

#11 by Amiram Eldar at Mon May 24 09:28:10 EDT 2021

MATHEMATICA

a[n_] := Sum[EulerPhi[k] * First @ Differences @ (Quotient[{n - 1, n}, k]^3) , , {k, 1, n}]; Array[a, 40] (* Amiram Eldar, May 24 2021 *)

STATUS

proposed

editing

#10 by Amiram Eldar at Mon May 24 09:27:53 EDT 2021

STATUS

editing

proposed

#9 by Amiram Eldar at Mon May 24 09:27:50 EDT 2021

MATHEMATICA

a[n_] := Sum[EulerPhi[k] * First @ Differences @ (Quotient[{n - 1, n}, k]^3) , {k, 1, n}]; Array[a, 40] (* Amiram Eldar, May 24 2021 *)

STATUS

proposed

editing

#8 by Seiichi Manyama at Mon May 24 09:11:41 EDT 2021

STATUS

editing

proposed

#7 by Seiichi Manyama at Mon May 24 08:04:27 EDT 2021

DATA

1, 8, 21, 46, 65, 126, 133, 224, 261, 364, 341, 618, 481, 722, 837, 1000, 833, 1404, 1045, 1718, 1641, 1798, 1541, 2760, 2065, 2516, 2673, 3346, 2465, 4410, 2821, 4256, 4041, 4312, 4469, 6462, 4033, 5390, 5637, 7504, 4961, 8532, 5461, 8186, 8613, 7906, 6533, 11736, 7861, 10640, 9621

#6 by Seiichi Manyama at Mon May 24 08:03:44 EDT 2021

PROG

(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k*(1+4*x^k+x^(2*k))/(1-x^k)^3))

#5 by Seiichi Manyama at Mon May 24 08:03:05 EDT 2021

FORMULA

G.f.: Sum_{k >= 1} phi(k) * x^k * (1 + 4*x^k + x^(2*k))/(1 - x^k)^3.

#4 by Seiichi Manyama at Mon May 24 08:02:23 EDT 2021

FORMULA

Sum_{k=1..n} a(k) = A344522(n).

CROSSREFS

Cf. A344522, A344598, A344600.