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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.
4
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
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 21 2014
STATUS
approved