A366245 The largest infinitary divisor of n that is a term of A366243.

1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 4, 1, 1, 1, 1, 1, 9, 1, 4, 1, 1, 1, 4, 25, 1, 9, 4, 1, 1, 1, 1, 1, 1, 1, 36, 1, 1, 1, 4, 1, 1, 1, 4, 9, 1, 1, 1, 49, 25, 1, 4, 1, 9, 1, 4, 1, 1, 1, 4, 1, 1, 9, 4, 1, 1, 1, 4, 1, 1, 1, 36, 1, 1, 25, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1

Offset

1,4

Comments

First differs from A335324 at n = 256.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = p^A063695(e).

a(n) = n / A366244(n).

a(n) >= 1, with equality if and only if n is a term of A366242.

a(n) <= n, with equality if and only if n is a term of A366243.

From Peter Munn, Jan 09 2025: (Start)

a(n) = max({k in A366243 : A059895(k, n) = k}).

a(n) = Product_{k >= 0} A352780(n, 2k+1).

Also defined by:

- for n in A046100, a(n) = A008833(n);

- a(n^4) = (a(n))^4;

- a(A059896(n,k)) = A059896(a(n), a(k)).

Other identities:

a(n) = sqrt(A366244(n^2)).

a(A059897(n,k)) = A059897(a(n), a(k)).

a(A225546(n)) = A225546(A248101(n)).

(End)

Mathematica

f[p_, e_] := p^BitAnd[e, Sum[2^k, {k, 1, Floor@ Log2[e], 2}]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) s(e) = -sum(k = 1, e, (-2)^k*floor(e/2^k));
a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^s(f[i, 2])); }

Crossrefs

Cf. A063695, A335324, A366242, A366243, A366244.

See the formula section for the relationships with A008833, A046100, A059895, A059896, A059897, A225546, A248101, A352780.

Sequence in context: A131301 A350698 A335324 * A083730 A373440 A358272

Adjacent sequences: A366242 A366243 A366244 * A366246 A366247 A366248

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 05 2023

Status

approved