OFFSET
1,4
COMMENTS
The number of divisors d of n that are infinitarily relatively prime to n (see A064379), i.e., d have no common infinitary divisors with n.
Equivalently, the number of divisors d of n such that for each prime divisor p of d, bitand(v_p(n), v_p(d)) = 0, where v_p(k) is the highest power of p that divides k. Note that for infinitary divisors d of n (A077609), bitand(v_p(n), v_p(d)) = v_p(d).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
MATHEMATICA
f[p_, e_] := 2^DigitCount[e, 2, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> 2^(logint(x, 2) + 1 - hammingweight(x)), factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Apr 28 2024
STATUS
approved