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A338558
Absolute value q such that tau(p) == q (mod p), where p = prime(n) and tau(i) = A000594(i).
1
0, 0, 0, 0, 1, 5, 7, 7, 1, 5, 10, 6, 11, 12, 20, 24, 14, 12, 3, 19, 6, 37, 20, 33, 20, 27, 50, 34, 36, 29, 18, 64, 4, 2, 66, 32, 3, 64, 61, 51, 60, 84, 95, 83, 63, 97, 42, 28, 61, 67, 32, 10, 29, 73, 37, 92, 16, 120, 31, 107, 120, 141, 145, 39, 12, 74, 150
OFFSET
1,6
COMMENTS
a(n) = 0 iff p is a term of A007659.
These are essentially the values that can be used to define "near-misses" in a search of terms for A007659, similar to how "near-Wieferich primes", "near-Wilson primes" and "near-Wall-Sun-Sun primes" are defined in searches for Wieferich primes (A001220), Wilson primes (A007540) and Wall-Sun-Sun (Fibonacci-Wieferich) primes.
LINKS
N. Lygeros and O. Rozier, A new solution for the equation tau(p)=0 (mod p), Journal of Integer Sequences 13 (2010), Article 10.7.4.
PROG
(PARI) a(n) = my(p=prime(n)); abs(centerlift(Mod(ramanujantau(p), p)))
CROSSREFS
A-values: A258367 (near-Wieferich), A250406 (near-Wilson), A244801 and A241014 (near-Wall-Sun-Sun), A260209 and A260210 (near-Wolstenholme).
Sequence in context: A138306 A197257 A217175 * A173930 A154802 A210624
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Dec 21 2020
STATUS
approved