A064030
Product of unitary divisors of n!.
Original entry on oeis.org
1, 2, 36, 576, 207360000, 268738560000, 416336312719673760153600000000, 6984964247141514123629140377600000000, 300679807141675805997423113304381849600000000
Offset: 1
n = 6 has 8 unitary divisors:{16,45,9,80,5,144,1,720}, a(6) = 720^4 = 268738560000
A064031
Product of non-unitary divisors of n!.
Original entry on oeis.org
1, 1, 1, 576, 207360000, 26956124946896309452800000000000, 2841003716170671644367609186370356458508919205193278721884160000000000000000000000
Offset: 1
n=6: 720 has 22 non-unitary divisors: a(6)=720^11=26956124946896309452800000000000
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a[n_] := (n!)^(DivisorSigma[0, n!]/2 - 2^(PrimePi[n]-1)); Array[a, 10] (* Amiram Eldar, Jul 16 2019 *)
A064032
Product of unitary divisors of binomial(n, floor(n/2)).
Original entry on oeis.org
1, 2, 3, 36, 100, 400, 1225, 24010000, 252047376, 4032758016, 2075562447064149770496, 531343986448422341246976, 75186222935463997063888896, 19247673071478783248355557376, 2940278105018015412903875390625, 566574142904620264536665169363475932852029446342410000000000000000
Offset: 1
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f[n_] := n^(2^(PrimeNu[n]-1)); Table[f[Binomial[n, Floor[n/2]]], {n, 1, 20}] (* Amiram Eldar, Jul 22 2024 *)
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a(n) = apply(x -> x^(2^(omega(x)-1)), binomial(n, n\2)); \\ Amiram Eldar, Jul 22 2024
A064033
Product of non-unitary divisors of binomial(n, floor(n/2)) or a(n) = 1 if all divisors are unitary. See A046098.
Original entry on oeis.org
1, 1, 1, 1, 1, 20, 1, 1, 15876, 1016255020032, 1, 728933458176, 8670998958336, 19247673071478783248355557376, 1714723915100625, 752711194884611945703392100000000, 1, 31226235883841773375939805209600000000, 1, 1357651828905889565182743230460164655087616
Offset: 1
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f[n_] := n^((DivisorSigma[0, n] - 2^PrimeNu[n]) / 2); Table[f[Binomial[n, Floor[n/2]]], {n, 1, 20}] (* Amiram Eldar, Jul 22 2024 *)
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a(n) = apply(x -> x^((numdiv(x) - 2^omega(x))/2), binomial(n, n\2)); \\ Amiram Eldar, Jul 22 2024
Showing 1-4 of 4 results.