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

1,2

Comments

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

Links

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

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).

Example

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

Mathematica

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

Prog

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

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)).

Sequence in context: A371932 A371639 A094347 * A288208 A024577 A121222

Adjacent sequences: A236283 A236284 A236285 * A236287 A236288 A236289

Keyword

nonn

Author

Jaroslav Krizek, Jan 21 2014

Status

approved