A375324 Numbers of the form 3^k + 2 that admit at least one divisor of the form 3^m + 2 with 1 <= m < k.

245, 2189, 19685, 531443, 1594325, 129140165, 10460353205, 31381059611, 847288609445, 7625597484989, 68630377364885, 617673396283949, 1853020188851843, 5559060566555525, 450283905890997365, 36472996377170786405, 109418989131512359211, 2954312706550833698645

Offset: 1

Author

Marius A. Burtea, Sep 15 2024

Keywords

• nonn

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.

Examples

			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.
		

Links

• Balkan Mathematical Olympiad, 2024, Problems

Crossrefs

Cf. A168607.

Programs

Magma

f:=func; [n:n in [3^a+2:a in [1..50]]|exists{d: d in Divisors(n)|d ne n and f(d-2) }];