A367419 a(n) = sqrt(A367418(n)).

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset

1,7

Links

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

Michael De Vlieger, Plot f(a(n)) at (x,y) = (n mod m, floor(n/m)) for m = 857 and n = 734449, where f is a color function such that 1 = gray, red indicates primes, gold composite prime powers, green squarefree composites, blue and purple numbers neither squarefree nor prime powers, but purple additionally represents squareful numbers that are not prime powers.

Formula

a(n) = sqrt(A003557(A268335(n))) = sqrt(A268335(n)/A367417(n)).

a(n) = A268335(n)/A367407(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/A065463 = 1.41956288050548591931... . - Amiram Eldar, Nov 17 2023

Mathematica

s[n_] := Sqrt[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(sqrtint(b1), ", "))); }

Crossrefs

Cf. A003557, A065463, A268335, A367407, A367417, A367418.

Sequence in context: A131789 A108465 A372467 * A069347 A161606 A300362

Adjacent sequences: A367416 A367417 A367418 * A367420 A367421 A367422

Keyword

nonn,easy

Author

Amiram Eldar, Nov 17 2023

Status

approved