Zachary M Franco has authored 3 sequences.
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
4 is a term because 4! = 24 and (2+4)/2 = 3 is an integer.
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q:= n-> (f-> (add(i, i=convert(f, base, 10))/length(f))::integer)(n!):
select(q, [$0..1000])[]; # Alois P. Heinz, Dec 19 2021
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Do[If[IntegerQ[Mean[IntegerDigits[n!]]], Print[n, " ", Mean[IntegerDigits[n!]]]], {n, 1, 100000}]
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isok(k) = my(d=digits(k!)); (vecsum(d) % #d) == 0; \\ Michel Marcus, Dec 19 2021
A322158
a(n) is the smallest m for which binomial(m,5) has exactly n distinct prime factors.
Original entry on oeis.org
6, 9, 11, 22, 25, 70, 78, 276, 497, 990, 1771, 8178, 20504, 44254, 181051, 416328, 1013728, 3383579, 8667726, 34332376, 122289552, 244215150, 969751302, 1865174676, 6648863728, 26888317326, 107132035803
Offset: 2
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a[n_] := Module[{m = 5}, While[PrimeNu[Binomial[m, 5]] != n, m++]; m]; Array[a, 10, 2] (* Amiram Eldar, Nov 29 2018 *)
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a(n) = for(m=5, oo, if(omega(binomial(m, 5))==n, return(m))) \\ Felix Fröhlich, Dec 01 2018
A321852
a(n) is the smallest m for which binomial(m, 6) has exactly n distinct prime factors.
Original entry on oeis.org
6, 7, 8, 9, 10, 18, 26, 40, 77, 120, 210, 477, 715, 2227, 3290, 9065, 17020, 49915, 139195, 240465, 721929, 1124840, 4455445, 16319578, 26683220, 105655905, 134879176, 677868170, 3290262264
Offset: 0
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a[n_] := Module[{m=6, t=1}, While[PrimeNu[t] != n, m++; t*=m/(m-6)]; m]; Array[a, 20] (* Amiram Eldar, Nov 27 2018 *)
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a(n)={my(m=6, t=1); while(omega(t)<>n, m++; t*=m/(m-6)); m} \\ Andrew Howroyd, Nov 26 2018
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