The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343497 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A343497

a(n) = Sum_{k=1..n} gcd(k, n)^3.
(history; published version)

#52 by Alois P. Heinz at Mon Jun 24 18:37:18 EDT 2024

STATUS

proposed

approved

#51 by G. C. Greubel at Mon Jun 24 18:13:42 EDT 2024

STATUS

editing

proposed

#50 by G. C. Greubel at Mon Jun 24 18:13:11 EDT 2024

MATHEMATICA

A343497[n_]:= DivisorSum[n, #^3*EulerPhi[n/#] &]; Table[A343497[n], {n, 50}] (* G. C. Greubel, Jun 24 2024 *)

PROG

(Magma)

A343497:= func< n | (&+[d^3*EulerPhi(Floor(n/d)): d in Divisors(n)]) >;

[A343497(n): n in [1..50]]; // G. C. Greubel, Jun 24 2024

(SageMath)

def A343497(n): return sum(k^3*euler_phi(n/k) for k in (1..n) if (k).divides(n))

[A343497(n) for n in range(1, 51)] # G. C. Greubel, Jun 24 2024

STATUS

approved

editing

#49 by Peter Bala at Mon Jan 29 08:29:28 EST 2024

LINKS

Peter Bala, <a href="/A368743/a368743.pdf">GCD sum theorems. Two Multivariable Cesaro Type Identities</a>.

STATUS

editing

approved

#48 by Peter Bala at Mon Jan 29 08:01:27 EST 2024

LINKS

Peter Bala, <a href="/A368743/a368743.pdf">GCD sum theorems. Two Multivariable Cesaro Type Identities</a>.

STATUS

approved

editing

#47 by Peter Luschny at Sun Jan 21 02:16:08 EST 2024

STATUS

reviewed

approved

#46 by Joerg Arndt at Sun Jan 21 01:29:20 EST 2024

STATUS

proposed

reviewed

#45 by Peter Bala at Sat Jan 20 16:10:33 EST 2024

STATUS

editing

proposed

#44 by Peter Bala at Sat Jan 20 16:10:08 EST 2024

MAPLE

with(numtheory):

seq(add(phi(n/d) * d^3, d in divisors(n)), n = 1..50); # Peter Bala, Jan 20 2024

#43 by Peter Bala at Sat Jan 20 16:08:11 EST 2024

FORMULA

a(n) = Sum_{1 <= i, j, k <= n} gcd(i, j, k, n) = Sum_{d divides n} d * J_3(n/d), where the Jordan totient function J_3(n) = A059376(n). - Peter Bala, Jan 20 2024

KEYWORD

nonn,mult,easy

STATUS

approved

editing