A329821 Largest k for which sigma(k) = A002191(n), where A002191 = range of sigma, the sum-of-divisors function A000203.

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, 39, 49, 59, 61, 32, 67, 71, 73, 45, 79, 83, 89, 36, 50, 77, 97, 101, 103, 107, 109, 91, 113, 95, 81, 75, 82, 64, 127, 131, 121, 137, 139, 119, 149, 151, 125

Offset

1,2

Links

Table of n, a(n) for n=1..61.

M. Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp, Oct. 2005

Formula

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

Example

The possible values of sigma(x) are A002191 = {1, 3, 4, 6, 7, 8, 12, ...}.
The 7th value is 12 = sigma(x) for x = 6 or 11. Since 11 is the largest such value, a(7) = 11.

Prog

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

Crossrefs

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

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

Sequence in context: A064620 A064216 A075300 * A353266 A259153 A355066

Adjacent sequences: A329818 A329819 A329820 * A329822 A329823 A329824

Keyword

nonn

Author

M. F. Hasler, Nov 22 2019

Status

approved