A329821 - OEIS

A329821

Largest k for which sigma(k) = A002191(n), where A002191 = range of sigma, the sum-of-divisors function A000203.

%I #17 Dec 26 2024 03:52:07

%S 1,2,3,5,4,7,11,9,13,8,17,19,23,12,29,25,31,22,37,18,27,41,43,47,53,

%T 39,49,59,61,32,67,71,73,45,79,83,89,36,50,77,97,101,103,107,109,91,

%U 113,95,81,75,82,64,127,131,121,137,139,119,149,151,125

%N Largest k for which sigma(k) = A002191(n), where A002191 = range of sigma, the sum-of-divisors function A000203.

%H Amiram Eldar, <a href="/A329821/b329821.txt">Table of n, a(n) for n = 1..10000</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).

%F a(n) = A085790(m,A054973(m)) with m = A002191(n).

%e The possible values of sigma(x) are A002191 = {1, 3, 4, 6, 7, 8, 12, ...}.

%e The 7th value is 12 = sigma(x) for x = 6 or 11. Since 11 is the largest such value, a(7) = 11.

%o (PARI) A329821(n)=vecmax(invsigma(A002191(n))) \\ see Alekseyev link for invsigma(). An invsigmaMax() function is announced.

%Y Cf. A000203 (sigma), A002191 (range of sigma), A085790 (table of pre-images of x in A002191), A054973 (number of solutions of sigma(x) = n).

%Y Cf. A051444 (smallest k such that sigma(k) = n).

%K nonn

%O 1,2

%A _M. F. Hasler_, Nov 22 2019