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A358545 a(n) is the smallest number with exactly n divisors that are centered square numbers. 4

%I #25 Dec 24 2022 19:05:11

%S 1,5,25,325,1625,1105,5525,27625,160225,1022125,801125,5928325,

%T 8491925,29641625,42459625,444215525,314201225,2003613625,1571006125,

%U 14826740825,12882250225,127081657625,64411251125,88717383625

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

%C Any subsequent terms are > 10^10. - _Lucas A. Brown_, Dec 24 2022

%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/CenteredSquareNumber.html">Centered Square Number</a>

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

%e a(3) = 25 because 25 has 3 centered square divisors {1, 5, 25} and this is the smallest such number.

%o (PARI) iscsq(n) = issquare(2*n-1); \\ A001844

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

%Y Cf. A001844, A005179, A130279, A300410, A358543, A358544.

%K nonn,more

%O 1,2

%A _Ilya Gutkovskiy_, Nov 21 2022

%E a(12)-a(15) from _Michel Marcus_, Nov 21 2022

%E a(16) from _Martin Ehrenstein_, Dec 02 2022

%E a(17)-a(24) from _Jinyuan Wang_, Dec 02 2022

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Last modified July 29 05:31 EDT 2024. Contains 374727 sequences. (Running on oeis4.)