A100879 a(n) = n^sigma(n).

1, 8, 81, 16384, 15625, 2176782336, 5764801, 35184372088832, 2541865828329, 1000000000000000000, 3138428376721, 1648446623609512543951043690496, 3937376385699289, 3214199700417740936751087616

Offset: 1

Author

Odimar Fabeny, Jan 09 2005

Keywords

• easy
• nonn

Examples

			a(1) = 1^1 = 1;
a(2) = 2^(1+2) = 8;
a(3) = 3^(1+3) = 81;
a(4) = 4^(1+2+4) = 16384.
		

Crossrefs

Cf. A000203, A192265.

Programs

Maple

with(numtheory): seq(n^add(d,d=divisors(n)),n=1..17); # C. Ronaldo, Jan 19 2005

Mathematica

Table[n^DivisorSigma[1,n],{n,20}] (* Harvey P. Dale, Oct 05 2011 *)

PARI

a(n)=n^sigma(n) \\ Charles R Greathouse IV, Aug 25 2014

Formula

a(n) = n^A000203(n). - Michel Marcus, Mar 17 2018

Sum_{n>=1} 1/a(n) = A192265. - Amiram Eldar, Nov 15 2020

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 19 2005