OFFSET
1,3
COMMENTS
Note that a(A005820(4)) = A005820(4) and a(A005820(6)) = A005820(6), i.e., the fourth and sixth 3-perfect numbers, 459818240 and 51001180160 are among the fixed points of this sequence, precisely because they are also terms of A323653. As the former factorizes as 459818240 = 256 * 5 * 7 * 19 * 37 * 73, it must follow that a(256)/256 * a(5)/5 * a(7)/7 * a(19)/19 * a(37)/37 * a(73)/73 = 1, because ratio a(n)/n is multiplicative. See also comments in A348738.
FORMULA
MATHEMATICA
s[n_] := n / 3^IntegerExponent[n, 3]; Table[s[DivisorSigma[1, n]], {n, 1, 100}] (* Amiram Eldar, Nov 04 2021 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 04 2021
STATUS
approved