A342024 a(n) = 1 if prime(k)^(k+1) divides n for some k, otherwise 0.

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Formula

a(n) = min(1, A276077(n)).

a(n) >= A342023(n).

a(n) <= A107078(n), i.e., a(n) = 1 => A107078(n) = 1.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - Product_{i>=1} 1-prime(i)^(-1-i) = 0.2789766... . - Amiram Eldar, Jul 24 2022

Mathematica

Table[Boole[Count[Prime[#]^(# + 1) & /@ Range[PrimePi@ Floor[Sqrt[n]]], _?(Mod[n, #] == 0 &)] > 0], {n, 120}] (* Michael De Vlieger, Mar 11 2021 *)

Prog

(PARI) A342024(n) = if(1==n, 0, my(f = factor(n)); for(k=1, #f~, if(f[k, 2]>primepi(f[k, 1]), return(1))); (0));
(Python)
from sympy import factorint, primepi
def A342024(n):
    f = factorint(n)
    for p in f:
        if primepi(p) < f[p]:
            return 1
    return 0 # Chai Wah Wu, Mar 09 2021

Crossrefs

Characteristic function of A276079.

Cf. A107078.

Differs from A129251 and A276077 for the first time at n=108, as here a(108) = 1.

Differs from A342023 for the first time at n=625, where a(625)=1, while A342023(625)=0.

Sequence in context: A188221 A011765 A342023 * A285464 A331282 A331169

Adjacent sequences: A342021 A342022 A342023 * A342025 A342026 A342027

Keyword

nonn

Author

Antti Karttunen, Mar 09 2021

Status

approved