A319068 a(n) is the greatest k such that A000203(k) divides n where A000203 is the sum of divisors of n.

1, 1, 2, 3, 1, 5, 4, 7, 2, 1, 1, 11, 9, 13, 8, 7, 1, 17, 1, 19, 4, 1, 1, 23, 1, 9, 2, 13, 1, 29, 25, 31, 2, 1, 4, 22, 1, 37, 18, 27, 1, 41, 1, 43, 8, 1, 1, 47, 4, 1, 2, 9, 1, 53, 1, 39, 49, 1, 1, 59, 1, 61, 32, 31, 9, 5, 1, 67, 2, 13, 1, 71, 1, 73, 8, 37, 4, 45, 1, 79

Offset

1,3

Comments

Sándor names this function the sum-of-divisors maximum function and remarks that this function is well-defined, since a(n) can be at least 1, and cannot be greater than n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

József Sándor, The sum-of-divisors minimum and maximum functions, Research Report Collection, Volume 8, Issue 1, 2005. See pp. 3-4.

Formula

a(p+1) = p, for p prime. See Sándor Theorem 2 p. 4.

Mathematica

A319068[n_] := Module[{k = n}, While[!Divisible[n, DivisorSigma[1, k]], k--]; k];
Array[A319068, 100] (* Paolo Xausa, Dec 11 2024 *)

Prog

(PARI) a(n) = {forstep (k=n, 1, -1, if ((n % sigma(k)) == 0, return (k)); ); }
(PARI) a(n) = {my(d = divisors(n)); vecmax(vector(#d, i, invsigmaMax(d[i]))); } \\ Amiram Eldar, Nov 29 2024, using Max Alekseyev's invphi.gp

Crossrefs

Cf. A000203 (sigma), A070982 (the sum of divisors minimum function).

Right border of A378912.

Sequence in context: A002472 A060116 A347120 * A335423 A345011 A345012

Adjacent sequences: A319065 A319066 A319067 * A319069 A319070 A319071

Keyword

nonn

Author

Michel Marcus, Sep 09 2018

Status

approved