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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.
0
31, 1310409, 298965241, 1939455002, 4578434282, 7077112564, 7973995681, 11430679681
OFFSET
1,1
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
KEYWORD
nonn,hard,more
AUTHOR
Michel Marcus, Feb 28 2021
EXTENSIONS
a(3)-a(8) from Jinyuan Wang, Feb 28 2021
STATUS
approved