A066449 -id:A066449 - cp's OEIS frontend

A064366 a(n) = binomial(sigma(n), phi(n)).

1, 3, 6, 21, 15, 66, 28, 1365, 1716, 3060, 66, 20475, 91, 134596, 735471, 7888725, 153, 3262623, 190, 118030185, 225792840, 254186856, 276, 2558620845, 84672315, 11058116888, 113380261800, 558383307300, 435, 11969016345, 496, 366395202809685, 16735679449896, 21094923659355

Offset: 1

Labos Elemer, Sep 27 2001

nonn

Harry J. Smith, Table of n, a(n) for n = 1..200

Cf. A000010, A000203, A000217, A034953, A066090, A066449.

Array[Binomial[DivisorSigma[1, #], EulerPhi@ #] &, 31] (* Michael De Vlieger, Nov 03 2017 *)

a(n) = { binomial(sigma(n), eulerphi(n)) } \\ Harry J. Smith, Sep 12 2009

a(n) = binomial(A000203(n), A000010(n));

a(p) = A000217(p) for prime p.

A066090 a(n) = binomial(sigma(n), n).

Original entry on oeis.org

1, 3, 4, 35, 6, 924, 8, 6435, 715, 43758, 12, 30421755, 14, 1961256, 1307504, 300540195, 18, 62359143990, 20, 513791607420, 129024480, 3796297200, 24, 36052387482172425, 736281, 166509721602, 12033222880, 7648690600760440, 30

Offset: 1

Joseph L. Pe, Dec 30 2001

			a(4) = binomial(sigma(4),4) = binomial(7,4) = 7!/(4!3!) = 35.

Harry J. Smith, Table of n, a(n) for n=1..200

Cf. A066449, A064366.

Table[ Binomial[ DivisorSigma[1, n], n], {n, 1, 32} ]

{ for (n=1, 200, a=binomial(sigma(n), n); write("b066090.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 12 2009

Corrected and extended by Robert G. Wilson v, Dec 31 2001

A204292 Binomial(n, d(n)), where d(n) = A000005(n) is the number of divisors of n.

Original entry on oeis.org

1, 1, 3, 4, 10, 15, 21, 70, 84, 210, 55, 924, 78, 1001, 1365, 4368, 136, 18564, 171, 38760, 5985, 7315, 253, 735471, 2300, 14950, 17550, 376740, 406, 5852925, 465, 906192, 40920, 46376, 52360, 94143280, 666, 73815, 82251, 76904685, 820, 118030185, 903, 7059052, 8145060

Offset: 1

Franklin T. Adams-Watters, Jan 14 2012

nonn

Cf. A000005, A066449, A068904.

Table[Binomial[n, DivisorSigma[0, n]], {n, 1, 50}] (* Vaclav Kotesovec, May 08 2021 *)

PARI
```
vector(60,n,binomial(n,numdiv(n)))
```

cp's OEIS Frontend

A064366 a(n) = binomial(sigma(n), phi(n)).

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Formula

A066090 a(n) = binomial(sigma(n), n).

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A204292 Binomial(n, d(n)), where d(n) = A000005(n) is the number of divisors of n.

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