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A369070
a(n) = 1 if there is at least one prime power p^e in the prime factorization of n such that p|e, otherwise 0.
3
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
FORMULA
For n >= 1, a(n) <= A342023(n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - Product_{p prime} (1 - (p - 1)/(p*(p^p - 1))) = 0.18824296270011399086... . - Amiram Eldar, Jan 15 2024
MAPLE
a:= n-> `if`(ormap(i-> irem(i[2], i[1])=0, ifactors(n)[2]), 1, 0):
seq(a(n), n=1..124); # Alois P. Heinz, Jan 15 2024
MATHEMATICA
a[n_] := If[AnyTrue[FactorInteger[n], Divisible[Last[#], First[#]] &], 1, 0]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jan 15 2024 *)
PROG
(PARI) A369070(n) = { my(f=factor(n)); for(i=1, #f~, if(!(f[i, 2]%f[i, 1]), return(1))); (0); };
(SageMath)
def isA369070(n): return any(f[1] % f[0] == 0 for f in factor(n))
print([int(isA369070(n)) for n in range(1, 101)]) # Peter Luschny, Jan 16 2024
CROSSREFS
Characteristic function of A342090.
Cf. A342023.
Sequence in context: A340599 A160753 A328981 * A024360 A025456 A288314
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 15 2024
STATUS
approved