A355821 Numbers k for which A003961(k) and A276086(k) are relatively prime, where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

1, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 33, 37, 41, 43, 47, 49, 53, 59, 61, 63, 67, 71, 73, 77, 79, 83, 89, 91, 93, 97, 101, 103, 107, 109, 113, 119, 121, 123, 127, 131, 133, 137, 139, 143, 149, 151, 153, 157, 161, 163, 167, 169, 173, 179, 181, 183, 187, 191, 193, 197, 199, 203, 209, 211, 213, 215, 221, 223, 227

Offset: 1

Author

Antti Karttunen, Jul 18 2022

Keywords

• nonn

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base

Crossrefs

Positions of 1's in A355442 and in A355001.

Cf. A003961, A276086, A355820 (characteristic function), A355822 (complement).

Cf. also A324583.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355820(n) = (1==gcd(A003961(n), A276086(n)));
isA355821(n) = A355820(n);

Python

from math import prod, gcd
from itertools import count, islice
from sympy import factorint, nextprime
def A355821_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        k = prod(nextprime(p)**e for p, e in factorint(n).items())
        m, p, c = 1, 2, n
        while c:
            c, a = divmod(c,p)
            m *= p**a
            p = nextprime(p)
        if gcd(k,m) == 1:
            yield n
A355821_list = list(islice(A355821_gen(),30)) # Chai Wah Wu, Jul 18 2022