A368329 The largest term of A054743 that divide n.

1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 16, 81, 1, 1, 1, 1

Offset

1,8

Comments

First differs from A360540 at n = 27.

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.

A034444(a(n)) = A368330(n).

a(n) >= 1, with equality if and only if n is in A207481.

a(n) <= n, with equality if and only if n is in A054743.

Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^((p+2)*s-1) - 1/p^((p+2)*(s-1)+1) - 1/p^((p+1)*s) + 1/p^((p+1)*(s-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

Cf. A054743, A034444, A207481, A327939, A360540, A368329, A368330, A368331, A368333.

Sequence in context: A368170 A366906 A056201 * A360540 A088842 A284098

Adjacent sequences: A368326 A368327 A368328 * A368330 A368331 A368332

Keyword

nonn,easy,mult

Author

Amiram Eldar, Dec 21 2023

Status

approved