A367418 The exponentially odd numbers (A268335) divided by their squarefree kernels (A007947).

1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 9, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 9, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1

Offset

1,7

Comments

Analogous to A102631, with the exponentially odd numbers instead of the square numbers (A000290).

All the terms are square numbers.

Links

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

Formula

a(n) = A003557(A268335(n)).

a(n) = A268335(n)/A367417(n).

a(n) = A367419(n)^2.

a(n) = A268335(n)^2/A367406(n).

a(n) = A008833(A268335(n)). - Amiram Eldar, Nov 30 2023

Mathematica

s[n_] := n / Times @@ FactorInteger[n][[;; , 1]]; s /@ Select[Range[200], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &]

Prog

(PARI) b(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%2, f[i, 1]^(f[i, 2]-1), 0)); }
lista(kmax) = {my(b1); for(k = 1, kmax, b1 = b(k); if(b1 > 0, print1(b1, ", "))); }

Crossrefs

Cf. A000290, A008833, A102631, A268335, A367406, A367417, A367419.

Sequence in context: A369935 A374325 A368169 * A360164 A360163 A336649

Adjacent sequences: A367415 A367416 A367417 * A367419 A367420 A367421

Keyword

nonn,easy

Author

Amiram Eldar, Nov 17 2023

Status

approved