A342118 Numbers k such that 1/(1/phi(k) + 1/phi(k+1) + 1/phi(k+2) + 1/phi(k+3) + 1/phi(k+4) + 1/phi(k+5)) is an integer.

31, 1310409, 298965241, 1939455002, 4578434282, 7077112564, 7973995681, 11430679681

Offset

1,1

Links

Table of n, a(n) for n=1..8.

Prog

(PARI) isok(k) = numerator(1/eulerphi(k) + 1/eulerphi(k+1) + 1/eulerphi(k+2) + 1/eulerphi(k+3) + 1/eulerphi(k+4) + 1/eulerphi(k+5)) == 1;
(Python)
from fractions import Fraction
from sympy import totient
k, plist, A342118_list = 1, [Fraction(1, totient(i)) for i in range(1, 7)], []
p = sum(plist)
while k < 10**7:
    if p.numerator == 1:
        A342118_list.append(k)
    k += 1
    p -= plist[0]
    plist = plist[1:] + [Fraction(1, totient(k+5))]
    p += plist[-1] # Chai Wah Wu, Mar 01 2021

Crossrefs

Cf. A000010, A073542, A073543, A073544, A341745.

Sequence in context: A123523 A079595 A051155 * A216791 A324268 A145210

Adjacent sequences: A342115 A342116 A342117 * A342119 A342120 A342121

Keyword

nonn,hard,more

Author

Michel Marcus, Feb 28 2021

Extensions

a(3)-a(8) from Jinyuan Wang, Feb 28 2021

Status

approved