A322585 a(n) = 1 if n is a product of primorial numbers (A002110), 0 otherwise.

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

Offset

1

Comments

Characteristic function of A025487, first differences of A085089.

a(n) = 1 if n = 2^e1 * 3^e2 * ... * prime(k)^e_k, with k = A061395(n) = A001221(n) and e1 >= e2 >= ... >= e_k, 0 otherwise.

Links

Antti Karttunen, Table of n, a(n) for n = 1..83160

Index entries for characteristic functions

Formula

For all n, a(n) >= A322586(n).

Prog

(PARI) A322585(n) = { my(f = factor(n)); for(i=1, #f~, if((primepi(f[i, 1])!=i)||((i>1)&&(f[i-1, 2]<f[i, 2])), return(0))); (1); };
(Python)
from sympy import primerange, factorint
def A322585(n):
    f = factorint(n)
    return int(list(f.keys())==(ps:=list(primerange(max(f, default=1)+1))) and all(f[ps[i]]>=f[ps[i+1]] for i in range(len(ps)-1))) # Chai Wah Wu, Mar 30 2026

Crossrefs

Cf. A001221, A002110, A025487, A061395, A085089 (partial sums), A322584, A322586.

Sequence in context: A141735 A343999 A344438 * A326956 A341629 A365429

Adjacent sequences: A322582 A322583 A322584 * A322586 A322587 A322588

Keyword

nonn

Author

Antti Karttunen, Dec 20 2018

Status

approved