The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A001817 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A001817

G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).
(history; published version)

#51 by Vaclav Kotesovec at Sat Nov 25 04:44:37 EST 2023

STATUS

reviewed

approved

#50 by Michel Marcus at Sat Nov 25 04:14:39 EST 2023

STATUS

proposed

reviewed

#49 by Amiram Eldar at Sat Nov 25 03:38:58 EST 2023

STATUS

editing

proposed

#48 by Amiram Eldar at Sat Nov 25 03:26:45 EST 2023

FORMULA

Sum_{k=1..n} a(k) = n*log(n)/3 + c*n + O(2*(3*n)^(1/3)*log(n)), where c = gamma(1,3) - (1 - gamma)/3 = A256425 - (1 - A001620)/3 = 0.536879... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

#47 by Amiram Eldar at Sat Nov 25 03:12:03 EST 2023

FORMULA

Sum_{k=1..n} a(k) = n*log(n)/3 + c * n + O(2*(3*n)^(1/3)*log(n)), where c = gamma(1,3) - (1 - gamma)/3 = A256425 - (1 - A001620)/3 = 0.536879... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

#46 by Amiram Eldar at Sat Nov 25 02:37:02 EST 2023

KEYWORD

nonn,easy,changed

#45 by Amiram Eldar at Sat Nov 25 02:29:22 EST 2023

REFERENCES

B. Bruce C. Berndt, On a certain theta-function in a letter of Ramanujan from Fitzroy House, Ganita 43 (1992), 33-43.

LINKS

Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>.

#44 by Amiram Eldar at Sat Nov 25 02:28:42 EST 2023

LINKS

R. A. Smith and M. V. Subbarao, <a href="https://doi.org/10.4153/CMB-1981-005-3">The average number of divisors in an arithmetic progression</a>, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.

FORMULA

Sum_{k=1..n} a(k) = n*log(n)/3 + c * n + O(2*(3*n)^(1/3)*log(n)), where c = gamma(1,3) - (1 - gamma)/3 = A256425 - (1 - A001620)/3 = 0.536879... (Smith and Subbarao, 1981). - Amiram Eldar, Nov 25 2023

CROSSREFS

Cf. A001620, A256425.

STATUS

approved

editing

#43 by Sean A. Irvine at Sat Jun 01 18:46:39 EDT 2019

STATUS

reviewed

approved

#42 by Jon E. Schoenfield at Sat Jun 01 13:57:24 EDT 2019

STATUS

proposed

reviewed