OFFSET
1,2
COMMENTS
The exponential unitary (or e-unitary) divisors of n = Product p(i)^a(i) are all the numbers of the form Product p(i)^b(i) where b(i) is a unitary divisor of a(i).
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
Nicusor Minculete and László Tóth, Exponential unitary divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 35 (2011), pp. 205-216.
FORMULA
Multiplicative with a(p^e) = Sum_{d|e, gcd(d, e/d)==1} p^d.
MATHEMATICA
f[p_, e_] := DivisorSum[e, p^# &, GCD[#, e/#]==1 &]; eusigma[n_] := Times @@ f @@@ FactorInteger[n]; Array[eusigma, 100]
PROG
(PARI) ff(p, e) = sumdiv(e, d, if (gcd(d, e/d)==1, p^d));
a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = ff(f[k, 1], f[k, 2]); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Dec 29 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Amiram Eldar, Dec 29 2018
STATUS
approved