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A358539 a(n) is the smallest number with exactly n divisors that are n-gonal numbers. 3

%I #20 Dec 14 2022 09:07:58

%S 6,36,210,1260,6426,3360,351000,207900,3749460,1153152,15036840,

%T 204204000,213825150,11737440,91797866160,1006485480,2310808500,

%U 4966241280,22651328700,325269404460,14266470332400,11203920000,256653797400,45843256859400,59207908359600,46822406400

%N a(n) is the smallest number with exactly n divisors that are n-gonal numbers.

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/figuratedivisors.py">Python program</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%e a(5) = 210 because 210 has 5 pentagonal divisors {1, 5, 35, 70, 210} and this is the smallest such number.

%o (PARI) a(n) = my(k=1); while (sumdiv(k, d, ispolygonal(d, n)) != n, k++); k; \\ _Michel Marcus_, Nov 21 2022

%Y Cf. A005179, A130279, A130317, A356132, A358540, A358541.

%K nonn

%O 3,1

%A _Ilya Gutkovskiy_, Nov 21 2022

%E a(12)-a(13) from _Michel Marcus_, Nov 21 2022

%E a(14)-a(16) from _Daniel Suteu_, Dec 04 2022

%E a(17)-a(28) from _Martin Ehrenstein_, Dec 05 2022

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Last modified June 11 18:20 EDT 2024. Contains 373315 sequences. (Running on oeis4.)