A165797 a(n) = n^( sigma(n) - tau(n) ).

1, 2, 9, 256, 625, 1679616, 117649, 8589934592, 3486784401, 100000000000000, 25937424601, 552061438912436417593344, 23298085122481, 83668255425284801560576, 332525673007965087890625

Offset: 1

Author

Jaroslav Krizek, Sep 27 2009

Keywords

• nonn

Comments

The power of n with exponent given by the difference between its sum of divisors and its count of divisors.

Examples

			a(4) = 4^(sigma(4)-tau(4)) = 4^(7-3) = 4^4 = 256.
		

Links

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

Programs

Mathematica

Table[n^[ DivisorSigma[1, n] - DivisorSigma[0, n]], {n, 50}]

Formula

a(n) = n^(A000203(n)-A000005(n)) = n^A000203(n) / n^A000005(n) = n^A065608(n).

a(n) = A100879(n) / A062758(n).

a(p) = p^(p-1) for p = prime.

Extensions

Slightly edited by R. J. Mathar, Sep 29 2009