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A341668
a(n) is the number of divisors of prime(n)^7 - 1.
1
2, 4, 6, 16, 16, 12, 10, 24, 16, 18, 16, 36, 32, 48, 16, 24, 64, 24, 32, 48, 24, 128, 16, 16, 96, 36, 64, 32, 96, 60, 144, 64, 32, 64, 12, 48, 48, 20, 16, 24, 16, 144, 128, 56, 96, 192, 96, 128, 32, 48, 64, 96, 80, 16, 72, 32, 192, 64, 96, 192, 32, 48, 48, 64
OFFSET
1,1
COMMENTS
a(n) >= A309906(7) = 8 for n > 3.
FORMULA
a(n) = A000005(A000040(n)^7 - 1).
EXAMPLE
p = factorization
n prime(n) p^7 - 1 of p^7 - 1 a(n)
- -------- ---------- --------------------- ----
1 2 127 127 2
2 3 2186 2 * 1093 4
3 5 78124 2^2 * 19531 6
4 7 823542 2 * 3 * 29 * 4733 16
5 11 19487170 2 * 5 * 43 * 45319 16
6 13 62748516 2^2 * 3 * 5229043 12
7 17 410338672 2^4 * 25646167 10
8 19 893871738 2 * 3^2 * 701 * 70841 24
9 23 3404825446 2 * 11 * 29 * 5336717 16
MATHEMATICA
a[n_] := DivisorSigma[0, Prime[n]^7 - 1]; Array[a, 50] (* Amiram Eldar, Feb 27 2021 *)
PROG
(PARI) a(n) = numdiv(prime(n)^7-1); \\ Michel Marcus, Feb 27 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Feb 26 2021
STATUS
approved