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A061555 Integer part of sigma(n!)/n!. 1

%I #28 Oct 03 2022 14:34:31

%S 1,1,1,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,

%T 6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,

%U 7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Integer part of sigma(n!)/n!.

%C With increasing n, a(n) goes to infinity (proof in Sierpiński).

%C From _Bernard Schott_, Oct 03 2022: (Start)

%C It seems that sigma(n!)/n! is an integer only for n = 0, 1, 3, 5 and corresponding values are 1, 1, 2, 3.

%C For m >= 2, the smallest integer n such that a(n) = m is A061556(m). (End)

%D Wacław Sierpiński, Elementary Theory of Numbers, Ex. 6, p. 169, Warsaw, 1964.

%H Harry J. Smith, <a href="/A061555/b061555.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = floor(sigma(n!)/n!) = floor(A062569(n)/A000142(n)).

%o (PARI) { for (n=0, 1000, write("b061555.txt", n, " ", sigma(n!)\n!) ) } \\ _Harry J. Smith_, Jul 24 2009

%Y Cf. A000142, A000203, A061556, A062569.

%K nonn

%O 0,4

%A _Labos Elemer_, May 17 2001

%E Terms corrected for an offset of 0 by _Harry J. Smith_, Jul 24 2009

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)