A004152 -id:A004152 - cp's OEIS frontend

A300659 Product of digits of n!.

1, 1, 2, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Jaroslav Krizek, Jun 05 2018

Also multiplicative digital root of n!.

Decimal expansion of 2817/25000. - Eric Chen, Jun 06 2018

Index entries for linear recurrences with constant coefficients, signature (1).

Cf. A000142, A007954, A031347, A067067, A086358, A004152.

[&*Intseq(Factorial(n)): n in [0..100]];

Array[Times @@ IntegerDigits[#!] &, 105] (* Michael De Vlieger, Jun 06 2018 *)

a(n) = my(d=digits(n!)); prod(k=1, #d, d[k]); \\ Michel Marcus, Jun 05 2018

G.f.: 1 + x + 2*x^2 + 6*x^3 + 8*x^4.
a(n) = 0 for n >= 5.
a(n) = A031347(A000142(n)).
a(n) = A007954(A000142(n)). - Eric Chen, Jun 06 2018

A349597 a(n) is the sum of digits of a(n-1)! with a(1) = 3.

Original entry on oeis.org

3, 6, 9, 27, 108, 666, 6327, 88263, 1692585, 42219558, 1318791681

Offset: 1

Arkady Pogostkin, Nov 22 2021

Subsequence of A008585.

Cf. A004152.

nterms=10;NestList[Total[IntegerDigits[#!]]&,3,nterms-1] (* Paolo Xausa, Nov 30 2021 *)

a(n) = sumdigits(a(n-1)!) for n > 1.

a(10)-a(11) from Amiram Eldar, Nov 23 2021

A350211 Numbers k such that the arithmetic mean of the digits of k! is an integer.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 12, 26, 28, 32, 59, 262, 391, 533, 579

Offset: 1

Zachary M Franco, Dec 19 2021

A heuristic argument suggests that this short list is complete. By Stirling's approximation, n! has order n*log(n) digits of which n/4 are terminal zeros. If the remaining digits are random, the mean will be just below 4.5. For n > 6, n! and also its digits sum are divisible by 9. 12! is the only factorial with 9 digits. The others have 27, 30, 36, 81, 522, 846, 1224, and 1350 digits, respectively.

			4 is a term because 4! = 24 and (2+4)/2 = 3 is an integer.

Cf. A000142, A004152, A034886, A058814, A061383.

q:= n-> (f-> (add(i, i=convert(f, base, 10))/length(f))::integer)(n!):
select(q, [$0..1000])[];  # Alois P. Heinz, Dec 19 2021

Do[If[IntegerQ[Mean[IntegerDigits[n!]]], Print[n, " ", Mean[IntegerDigits[n!]]]], {n, 1, 100000}]

isok(k) = my(d=digits(k!)); (vecsum(d) % #d) == 0; \\ Michel Marcus, Dec 19 2021

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A300659 Product of digits of n!.

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A349597 a(n) is the sum of digits of a(n-1)! with a(1) = 3.

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A350211 Numbers k such that the arithmetic mean of the digits of k! is an integer.

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