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A319068 a(n) is the greatest k such that A000203(k) divides n where A000203 is the sum of divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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.

PROG

(PARI) a(n) = {forstep (k=n, 1, -1, if ((n % sigma(k)) == 0, return (k)); ); }

CROSSREFS

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

Sequence in context: A336365 A002472 A060116 * A335423 A114690 A336364

Adjacent sequences:  A319065 A319066 A319067 * A319069 A319070 A319071

KEYWORD

nonn

AUTHOR

Michel Marcus, Sep 09 2018

STATUS

approved

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Last modified May 7 16:00 EDT 2021. Contains 343652 sequences. (Running on oeis4.)