A236285
a(n) = tau(n)^sigma(n), where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.
Original entry on oeis.org
1, 8, 16, 2187, 64, 16777216, 256, 1073741824, 1594323, 68719476736, 4096, 6140942214464815497216, 16384, 281474976710656, 281474976710656, 4656612873077392578125, 262144, 2227915756473955677973140996096, 1048576, 481229803398374426442198455156736
Offset: 1
a(4) = tau(4)^sigma(4) = 3^7 = 2187.
-
Table[DivisorSigma[0, n]^DivisorSigma[1, n], {n, 1000}]
-
s=[]; for(n=1, 20, s=concat(s, sigma(n, 0)^sigma(n))); s \\ Colin Barker, Jan 22 2014
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.
Original entry on oeis.org
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
a(4) = tau(4)^sigma(4) / tau(4)^4 = 3^7 /3^4 = 27.
-
Table[DivisorSigma[0, n]^[DivisorSigma[1, n] - n], {n, 1000}]
-
s=[]; for(n=1, 30, s=concat(s, sigma(n, 0)^sigma(n)/sigma(n, 0)^n)); s \\ Colin Barker, Jan 22 2014
A331667
Numbers m with a divisor d such that tau(d)^d = m.
Original entry on oeis.org
1, 4, 19683, 65536, 2176782336, 101559956668416, 7958661109946400884391936
Offset: 1
19683 is a term because 3^9 = 19683; 9 divides 19683, tau(9) = 3.
-
[n: n in [1..100000] | #[d: d in Divisors(n) | NumberOfDivisors(d)^d eq n] ge 1]
-
seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #]^# == n &]; Select[Range[70000], seqQ] (* Amiram Eldar, Feb 28 2020 *)
-
isok(m) = fordiv(m, d, if (numdiv(d)^d == m, return (1));); \\ Michel Marcus, Mar 07 2020
Showing 1-3 of 3 results.
Comments