A236286 a(n) = tau(n)^sigma(n) / tau(n)^n, where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.

1, 2, 2, 27, 2, 4096, 2, 16384, 81, 65536, 2, 2821109907456, 2, 1048576, 262144, 30517578125, 2, 21936950640377856, 2, 131621703842267136, 4194304, 268435456, 2, 324518553658426726783156020576256, 729, 4294967296, 67108864, 6140942214464815497216, 2

Offset: 1

Author

Jaroslav Krizek, Jan 21 2014

Keywords

• nonn

Comments

a(n) = tau(n)^sigma_p(n), where sigma_p(n) = A001065(n) = the sum of proper divisors of n.

Examples

			a(4) = tau(4)^sigma(4) / tau(4)^4 = 3^7 /3^4 = 27.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A000005 (tau(n)), A000203 (sigma(n)), A001065 (sigma_p(n)), A062758 (n^tau(n)), A217872 (sigma(n)^n), A236284 (tau(n)^n), A236285 (tau(n)^sigma(n)).

Programs

Mathematica

Table[DivisorSigma[0, n]^[DivisorSigma[1, n] - n], {n, 1000}]

PARI

s=[]; for(n=1, 30, s=concat(s, sigma(n, 0)^sigma(n)/sigma(n, 0)^n)); s \\ Colin Barker, Jan 22 2014

Formula

a(n) = A236285(n) / A236284(n) = A000005(n)^A000203(n) / A000005(n)^n = A000005(n)^A001065(n).

a(p) = 2 for p = primes (A000040).