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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.
6
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
1,2
PROG
(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
CROSSREFS
Positions of 1's in A355442 and in A355001.
Cf. A003961, A276086, A355820 (characteristic function), A355822 (complement).
Cf. also A324583.
Sequence in context: A318718 A118749 A367227 * A332075 A122089 A109860
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 18 2022
STATUS
approved