A361627 Positive integers such that GCD(A007504(n),n) != 1.

18, 23, 24, 25, 30, 36, 42, 53, 54, 56, 57, 63, 78, 84, 85, 90, 99, 105, 111, 117, 123, 126, 129, 138, 154, 170, 177, 180, 190, 195, 207, 213, 222, 228, 230, 237, 238, 240, 245, 246, 252, 258, 270, 273, 275, 276, 282, 288, 297, 299, 303, 304, 309, 318, 319, 322, 327, 333, 339, 345

Offset: 1

Author

Luca Onnis, Mar 18 2023

Keywords

• nonn

Comments

A301274(k) != k implies that k is a term of this sequence.

Conjecture: a(n) ~ C*n as n -> infinity, where 5.25 < C < 5.35.

Examples

			18 is a term of this sequence since the sum of the first 18 primes is 501 and GCD(501,18) = 3 != 1.
		

Crossrefs

Cf. A007504, A301274.

Programs

Mathematica

s[n_] := Sum[Prime[k], {k, 1, n}];
Complement[Table[n, {n, 1, 1000}], Flatten[Position[Table[GCD[s[n], n], {n, 1, 1000}], 1]]]

PARI

isok(k) = gcd(vecsum(primes(k)), k) != 1; \\ Michel Marcus, Mar 18 2023

Python

from math import gcd
from itertools import count, islice
from sympy import nextprime
def A361627_gen(): # generator of terms
    p, s = 2, 2
    for n in count(1):
        if gcd(n,s) > 1:
            yield n
        s += (p:=nextprime(p))
A361627_list = list(islice(A361627_gen(),20)) # Chai Wah Wu, Mar 22 2023