OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)
FORMULA
a(n*m) = a(n) + a(m) - a(gcd(n^2, m)) - a(gcd(n, m^2)) for all n and m > 0 (conjecture). - Velin Yanev, Feb 17 2019
From Amiram Eldar, Jul 24 2024: (Start)
Additive with a(p^e) = p is e = 1, and 0 otherwise. (End)
EXAMPLE
The prime divisors of 420 = 2^2 * 3 * 5 * 7 that have exponent 1 (i.e., unitary prime divisors) are {3, 5, 7}, so a(420) = 3 + 5 + 7 = 15.
MATHEMATICA
Table[DivisorSum[n, # &, And[PrimeQ@ #, GCD[#, n/#] == 1] &], {n, 81}] (* Michael De Vlieger, Feb 17 2019 *)
f[p_, e_] := If[e == 1, p, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 24 2024 *)
PROG
(PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[2, i]==1, a+=f[1, i])); write("b063956.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 04 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Sep 04 2001
STATUS
approved