%I #22 Jan 07 2023 04:02:45

%S 1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,1,

%T 1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,

%U 1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1

%N Multiplicative with a(p^e) = 1 if p > e, otherwise 0.

%H Antti Karttunen, <a href="/A359550/b359550.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%F Multiplicative with a(p^e) = [e < p], where [ ] is the Iverson bracket.

%F a(n) = [A129251(n) == 0] = [A327936(n) == 1] = [A342007(n) == 1].

%F a(n) = 1 - A342023(n).

%F Sum_{k=1..n} a(k) ~ c * n, where c = Product_{p prime} (1 - 1/p^p) = 0.7219902344... . - _Amiram Eldar_, Jan 07 2023

%t f[p_, e_] := If[e < p, 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 06 2023 *)

%o (PARI) A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };

%o (Python)

%o from sympy import factorint

%o def A359550(n): return int(all(map(lambda d:d[0]>d[1],factorint(n).items()))) # _Chai Wah Wu_, Jan 06 2023

%Y Characteristic function of A048103.

%Y Cf. A129251, A327936, A328308, A342007, A342023 (one's complement), A359546, A359551 (Dirichlet inverse).

%K nonn,mult

%O 1

%A _Antti Karttunen_, Jan 06 2023