The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #20 Jun 25 2022 21:55:00
%S 1,4,9,32,25,216,49,512,243,1000,121,20736,169,2744,3375,16384,289,
%T 104976,361,160000,9261,10648,529,7962624,3125,17576,19683,614656,841,
%U 24300000,961,1048576,35937,39304,42875,362797056,1369,54872,59319,102400000,1681
%N a(n) = n * pod(n) where pod(n) = the product of divisors of n (A007955).
%F a(n) = n * A007955(n) = n^2 * A007956(n).
%F a(n) = lcm(n, pod(n)) * gcd(n, pod(n)).
%F a(p) = p^2 for p = primes (A000040).
%e a(6) = 6 * pod(6) = 6 * 36 = 216.
%t a[n_] := n^(1 + DivisorSigma[0, n]/2); Array[a, 50] (* _Amiram Eldar_, Nov 03 2020 *)
%o (Magma) [n * &*Divisors(n): n in [1..100]]
%o (PARI) a(n) = n*vecprod(divisors(n)); \\ _Michel Marcus_, Nov 03 2020
%o (Python)
%o from math import isqrt
%o from sympy import divisor_count
%o def A338576(n): return (isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2+1) # _Chai Wah Wu_, Jun 25 2022
%Y Cf. A007955 (pod(n)), A007956 (pod(n) / n).
%Y Similar sequences: A038040 (n * tau(n)), A064987 (n * sigma(n)).
%Y Cf. A174935 (partial sums of a(n)).
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Nov 03 2020