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

9, 225, 11025, 1334025, 225450225, 65155115025, 23520996524025, 12442607161209225, 9070660620521525025, 7628425581858602546025, 7330916984166117046730025, 10036025351323414236973404225, 16870558615574659332352292502225, 31193662880197545105519388836614025, 68906801302356377138092329940080381225

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Formula

a(prime(n) - 1) = A038547(A038547(prime(n))), n >= 1.

Example

a(3) = A038547(3^3) = 11025 = 3^2 * 5^2 * 7^2,
a(8) = A038547(3^8) = 12442607161209225 = 3^2 * ... * 23^2,
a(9) = A038547(3^9) = 9070660620521525025 = 3^8 * 5^2 * ... * 23^2 since 23^2 = 529 < 3^6 = 729 < 29^2 = 841,
a(10) = A038547(3^10) = 7628425581858602546025 = 3^8 * 5^2 * ... * 29^2.
a(31) = A038547(3^31) = 3^8 * 5^8 * 7^2 * ... * 113^2.
a(70) = A038547(3^70) = 3^8 * 5^8 * 7^8 * 11^2 * ... * 337^2.

Mathematica

value3[part_] := Module[{len=Length[part]}, Apply[Times, Map[#[[1]]^(3^#[[2]]-1)&, Transpose[{Map[Prime, Range[2, len+1]], part}]]]]
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]
Map[a360435, Range[15]]

Prog

(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

Crossrefs

Cf. A001227, A005179, A007051, A038547, A070826, A122842.

Sequence in context: A128492 A294971 A001818 * A369059 A095363 A138564

Adjacent sequences: A360432 A360433 A360434 * A360436 A360437 A360438

Keyword

nonn

Author

Hartmut F. W. Hoft, Feb 07 2023

Status

approved