OFFSET
1,4
COMMENTS
The largest divisor d of n such that e >= p for all prime powers p^e in the prime factorization of d (i.e., e >= 1 and p^(e+1) does not divide d).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = 1 if e < p, and a(p^e) = p^e if e >= p.
a(n) >= 1, with equality if and only if n is in A048103.
a(n) <= n, with equality if and only if n is in A054744.
Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) - 1/p^(p*s) + 1/p^(p*(s-1)) + 1/p^((p+1)*s-1) - 1/p^((p+1)*(s-1)+1)).
MATHEMATICA
f[p_, e_] := If[e < p, 1, p^e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] < f[i, 1], 1, f[i, 1]^f[i, 2])); }
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Dec 21 2023
STATUS
approved