OFFSET
1,2
COMMENTS
a(p) = p for p prime, since gcd(k,p) = 1 for 1 <= k < p, the product of k is also coprime to p, but multiples n*p for n >= 1 are plainly divisible by p. - Michael De Vlieger, Nov 22 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Michael De Vlieger)
FORMULA
MATHEMATICA
Table[If[PrimeQ@ b, b, Count[Flatten@ Array[# Range@ # &, b], _?(Mod[#, b] == 0 &)]], {b, 69}] (* Michael De Vlieger, Nov 22 2019 *)
f1[p_, e_] := (e*(p - 1)/p + 1)*p^e; f2[p_, e_] := p^Floor[e/2]; a[n_] := (Times @@ f1 @@@ (fct = FactorInteger[n]) + Times @@ f2 @@@ fct)/2; Array[a, 100] (* Amiram Eldar, Apr 28 2023 *)
PROG
(PARI) a(n)={ my(ct=0); for(i=0, n-1, for(j=0, i, ct+=(Mod(i*j, n)==0) ) ); ct; } \\ Joerg Arndt, Aug 03 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Russell Easterly, Mar 06 2010
EXTENSIONS
More terms from Max Alekseyev, Sep 05 2010
Better name from Joerg Arndt, Aug 03 2013
STATUS
approved