A360438 Smallest number with 2^n odd divisors.

1, 3, 15, 105, 945, 10395, 135135, 2297295, 43648605, 1003917915, 25097947875, 727840488375, 22563055139625, 834833040166125, 34228154646811125, 1471810649812878375, 69175100541205283625, 3389579926519058897625, 179647736105510121574125, 10599216430225097172873375, 646552202243730927545275875

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Hartmut F. W. Hoft, Computational Characterization of a(n) = A038547(2^n)

Formula

a(n) = A038547(2^n).

Example

a(4) = A038547(2^4) = 945 = 3^(2^2-1) * 5^(2^1-1) * 7^(2^1-1)  = 3^3 * 5 * 7,
a(5) = A038547(2^5) = 10395 = 3^(2^2-1) * 5^(2^1-1) * 7^(2^1-1) * 11^(2^1-1) = 3^3 * 5 * 7 * 11,
a(24) = 3^3 * 5^3 * 7^3 * 11 * ... *79, and
a(25) = 3^7 * 5^3 * 7^3 * 11 * ... *79 since 79 < 3^4 < 83.

Mathematica

next[{num_, fList_, lastP_, {p_, k_}}] := Module[{nP, f1List, p1, k1}, nP=NextPrime[First[Last[fList]]]; If[nP<p^k, {num nP, Append[fList, {nP, 1}], nP, {p, k}}, f1List=Replace[fList, {p, k-1}->{p, 2k-1}, {1}]; {{p1, k1}}=FactorInteger[Min[Map[#[[1]]^(#[[2]]+1)&, f1List]]]; {num p^k, f1List, lastP, {p1, k1}}]]
a360438[n_] := Join[{1}, Map[First, NestList[next, {3, {{3, 1}}, 3, {3, 2}}, n-1]]]/; n>=1
Join[{1}, a360438[20]]

Crossrefs

Cf. A005179, A038547.

Sequence in context: A294002 A001147 A330797 * A000268 A207818 A354218

Adjacent sequences: A360435 A360436 A360437 * A360439 A360440 A360441

Keyword

nonn

Author

Hartmut F. W. Hoft, Feb 07 2023

Status

approved