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A375324
Numbers of the form 3^k + 2 that admit at least one divisor of the form 3^m + 2 with 1 <= m < k.
0
245, 2189, 19685, 531443, 1594325, 129140165, 10460353205, 31381059611, 847288609445, 7625597484989, 68630377364885, 617673396283949, 1853020188851843, 5559060566555525, 450283905890997365, 36472996377170786405, 109418989131512359211, 2954312706550833698645
OFFSET
1,1
COMMENTS
The sequence is inspired by problem 3, Balkan Mathematical Olympiad 27 April - 2 May 2024, Varna, Bulgaria, (see link).
The sequence is infinite because numbers of the form m = 3^(4*k + 1) + 2 are divisible by 5 = 3^1 + 2.
LINKS
Balkan Mathematical Olympiad, 2024, Problems
EXAMPLE
245 = 3^5 + 2 and 245 = 49*5 = 49 * (3^1 + 2), so 245 is a term.
2189 = 3^7 + 2 and 2189 = 11*199 = 199 * (3^2 + 2), so 2189 is a term.
129140165 = 3^17 + 2 and 129140165 = 5*25828033 = (3^1 + 2)*25828033 or 129140165 = 11*11740015 = (3^2 + 2)*11740015, so 129140165 is a term.
PROG
(Magma) f:=func<n|PrimeDivisors(n) eq [3]>; [n:n in [3^a+2:a in [1..50]]|exists{d: d in Divisors(n)|d ne n and f(d-2) }];
CROSSREFS
Cf. A168607.
Sequence in context: A237161 A056264 A154080 * A259511 A023097 A098195
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Sep 15 2024
STATUS
approved