The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A344371 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A344371

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

#19 by Joerg Arndt at Sat Mar 30 03:00:33 EDT 2024

STATUS

reviewed

approved

#18 by Michel Marcus at Sat Mar 30 02:50:57 EDT 2024

STATUS

proposed

reviewed

#17 by Amiram Eldar at Sat Mar 30 02:42:57 EDT 2024

STATUS

editing

proposed

#16 by Amiram Eldar at Sat Mar 30 02:41:24 EDT 2024

CROSSREFS

Cf. A001620, A090423, A106475, A199084, A306016, A344372, A344373.

#15 by Amiram Eldar at Sat Mar 30 02:24:12 EDT 2024

FORMULA

Sum_{k=1..n} a(k) ~ (n^2/Pi^2) * (log(n) + 2*gamma - 1/2 - 4*log(2)/3 + Pi^2/4 - zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). - Amiram Eldar, Mar 30 2024

CROSSREFS

Cf. A001620, A090423, A106475, A199084, A344372, A344373.

STATUS

approved

editing

#14 by Peter Bala at Tue Dec 26 14:37:26 EST 2023

NAME

a(n) = Sum_{k = 1..n} (-1)^(n-k) gcd(k,n).

FORMULA

a(2*n2n+1) = 2*n 2n+ 1.

a(2*n2n) = A344372(n) = 2*n - A106475(n-1).

From Peter Bala, Dec 26 2023: (Start)

Conjectures:

1) for n >= 0, a(24*n+12) = 4*a(12*n+6) (checked up to n = 1000).

2) more generally, for n >= 0 and k >= 1, a((2^k)*(6*n+3)) = a(2^k)*a(12*n+6). (End)

MAPLE

a := n->sum((-1)^(n+k)*igcd(n, k), k = 1..n): seq(a(n), n = 1..50); # Peter Bala, Dec 26 2023

CROSSREFS

Cf. A018804, A090423, A069097, A106475, A199084, A343497, A343498, A343499, A344372, A344373.

KEYWORD

nonn,easy,changed

STATUS

editing

approved

#13 by Peter Bala at Tue Dec 26 11:37:02 EST 2023

CROSSREFS

Cf. A018804, A090423, A069097, A106475, A199084, A343497, A343498, A3343499, A343499, A344372, A344373.

#12 by Peter Bala at Tue Dec 26 11:36:12 EST 2023

NAME

a(n) = Sum_{k = 1..n} (-1)^(n-k) gcd(k,n).

FORMULA

a(2n2*n+1) = 2n2*n + 1.

a(2n2*n) = A344372(n) = 2*n - A106475(n-1).

From Peter Bala, Dec 26 2023: (Start)

Conjectures:

1) for n >= 0, a(24*n+12) = 4*a(12*n+6) (checked up to n = 1000).

2) more generally, for n >= 0 and k >= 1, a((2^k)*(6*n+3)) = a(2^k)*a(12*n+6). (End)

MAPLE

a := n->sum((-1)^(n+k)*igcd(n, k), k = 1..n): seq(a(n), n = 1..50); # Peter Bala, Dec 26 2023

CROSSREFS

Cf. A018804, A090423, A069097, A106475, A199084, A343497, A343498, A3343499, A344372, A344373.

STATUS

approved

editing

#11 by N. J. A. Sloane at Mon May 24 01:02:09 EDT 2021

STATUS

proposed

approved

#10 by Felix Fröhlich at Wed May 19 14:00:43 EDT 2021

STATUS

editing

proposed