cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A360435 a(n) = A038547(3^n), smallest number with 3^n odd divisors.

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%I A360435 #14 Feb 19 2023 22:19:29
%S A360435 9,225,11025,1334025,225450225,65155115025,23520996524025,
%T A360435 12442607161209225,9070660620521525025,7628425581858602546025,
%U A360435 7330916984166117046730025,10036025351323414236973404225,16870558615574659332352292502225,31193662880197545105519388836614025,68906801302356377138092329940080381225
%N A360435 a(n) = A038547(3^n), smallest number with 3^n odd divisors.
%F A360435 a(prime(n) - 1) = A038547(A038547(prime(n))), n >= 1.
%e A360435 a(3) = A038547(3^3) = 11025 = 3^2 * 5^2 * 7^2,
%e A360435 a(8) = A038547(3^8) = 12442607161209225 = 3^2 * ... * 23^2,
%e A360435 a(9) = A038547(3^9) = 9070660620521525025 = 3^8 * 5^2 * ... * 23^2 since 23^2 = 529 < 3^6 = 729 < 29^2 = 841,
%e A360435 a(10) = A038547(3^10) = 7628425581858602546025 = 3^8 * 5^2 * ... * 29^2.
%e A360435 a(31) = A038547(3^31) = 3^8 * 5^8 * 7^2 * ... * 113^2.
%e A360435 a(70) = A038547(3^70) = 3^8 * 5^8 * 7^8 * 11^2 * ... * 337^2.
%t A360435 value3[part_] := Module[{len=Length[part]}, Apply[Times, Map[#[[1]]^(3^#[[2]]-1)&, Transpose[{Map[Prime, Range[2, len+1]], part}]]]]
%t A360435 a360435[n_] := Module[{pL=Reverse[IntegerPartitions[n]], min, i=2, next}, min=value3[pL[[1]]]; While[i<=Length[pL]&&3^(3^pL[[i, 1]]-1)<min, next=value3[pL[[i]]]; If[next<min, min=next]; i++]; min]
%t A360435 Map[a360435, Range[15]]
%o A360435 (PARI) a(n)={my(m=vecprod(primes(n+1))^2/4, b=logint(logint(m,3)+1,3)); forpart(p=n, m=min(m, prod(i=1, #p, prime(1+i)^(3^p[#p+1-i]-1))), [1, b]); m} \\ _Andrew Howroyd_, Feb 07 2023
%Y A360435 Cf. A001227, A005179, A007051, A038547, A070826, A122842.
%K A360435 nonn
%O A360435 1,1
%A A360435 _Hartmut F. W. Hoft_, Feb 07 2023