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A368886 The largest unitary divisor of n without an exponent 2 in its prime factorization (A337050). 2
1, 2, 3, 1, 5, 6, 7, 8, 1, 10, 11, 3, 13, 14, 15, 16, 17, 2, 19, 5, 21, 22, 23, 24, 1, 26, 27, 7, 29, 30, 31, 32, 33, 34, 35, 1, 37, 38, 39, 40, 41, 42, 43, 11, 5, 46, 47, 48, 1, 2, 51, 13, 53, 54, 55, 56, 57, 58, 59, 15, 61, 62, 7, 64, 65, 66, 67, 17, 69, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^2) = 1, and a(p^e) = p^e if e != 2.
a(n) = n / A368884(n).
a(n) >= 1, with equality if and only if n is in A062503.
a(n) <= n, with equality if and only if n is in A337050.
Dirichlet g.f.: zeta(s-1) * Product_{p prime} (1 - 1/p^(2*s-2) + 1/p^(2*s) + 1/p^(3*s-3) - 1/p^(3*s-1)).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} (1 - 1/p^2 + 1/p^3 + 1/p^4 - 1/p^5) = 0.78357388280736936739... .
MATHEMATICA
f[p_, e_] := If[e == 2, 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] == 2, 1, f[i, 1]^f[i, 2])); }
(Python)
from math import prod
from sympy import factorint
def A368886(n): return prod(p**e for p, e in factorint(n).items() if e!=2) # Chai Wah Wu, Jan 09 2024
CROSSREFS
Sequence in context: A214392 A071975 A350389 * A182659 A359593 A358881
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Jan 09 2024
STATUS
approved

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Last modified July 9 09:56 EDT 2024. Contains 374174 sequences. (Running on oeis4.)