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.

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

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

Adjacent sequences: A369067 A369068 A369069 * A369071 A369072 A369073

Keyword

nonn

Author

Antti Karttunen, Jan 15 2024

Status

approved