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A341669 Primes p such that p^7 - 1 has 8 divisors. 1
863, 1439, 2039, 3167, 3803, 4799, 10559, 11423, 14087, 14207, 15287, 15803, 16139, 18743, 20663, 21059, 21179, 22343, 25307, 25919, 26459, 29483, 29759, 30803, 32507, 32987, 33107, 34319, 34367, 35879, 43427, 45887, 46559, 46643, 46919, 54959, 57119, 57587 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For each term p, p^7 - 1 = (p-1)*(p^6 + p^5 + p^4 + p^3 + p^2 + p + 1) is a number of the form 2*q*r (where q and r are distinct primes): p-1 = 2*q and p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 = r.
Conjecture: sequence is infinite.
LINKS
EXAMPLE
p =
n a(n) factorization of p^7 - 1
- ----- ------------------------------------
1 863 2 * 431 * 413588356833933793
2 1439 2 * 719 * 8885189025331426081
3 2039 2 * 1019 * 71897932302115976281
4 3167 2 * 1583 * 1009312223899992366817
5 3803 2 * 1901 * 3026022586778671180093
6 4799 2 * 2399 * 12217856103420111345601
7 10559 2 * 5279 * 1386046726502834819142721
8 11423 2 * 5711 * 2221872233870122705845793
9 14087 2 * 7043 * 7815232779386331437540137
MATHEMATICA
Select[Range[60000], PrimeQ[#] && DivisorSigma[0, #^7 - 1] == 8 &] (* Amiram Eldar, Feb 27 2021 *)
PROG
(PARI) isok(p) = isprime(p) && (numdiv(p^7-1) == 8); \\ Michel Marcus, Feb 27 2021
CROSSREFS
Sequence in context: A203272 A344288 A327378 * A344289 A344287 A252297
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Feb 26 2021
STATUS
approved

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Last modified July 23 09:37 EDT 2024. Contains 374547 sequences. (Running on oeis4.)