OFFSET
1,2
COMMENTS
If n = p_1^e_1 *p_2^e_2 *p_3^e_3 *...* p_m^e_m is the canonical prime factorization of n with e_1, e_2, e_3,.. >0 and p_1<p_2<p_3<...<p_m, then a(n) = p_1^(e_1-1) *p_2^(e_2-1) *... *p_m^e^m, where exponents of all prime factors are decremented by 1, with the exception of the exponent associated with the largest prime prime factor that stays intact.
All prime powers (A000961) are fixed points.
LINKS
Michel Marcus, Table of n, a(n) for n = 1..10000
EXAMPLE
For n=24 = 2^3*3, the exponent 3 (associated with the smaller prime 2) is reduced to 2, so a(n)=2^2*3=12.
MAPLE
PROG
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~-1, f[k, 2]--); factorback(f); \\ Michel Marcus, Jun 28 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Oct 02 2012
EXTENSIONS
a(71) corrected by Georg Fischer, Jun 28 2021
STATUS
approved