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

Author

Hartmut F. W. Hoft, Feb 07 2023

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A005179, A038547.

Programs

Mathematica

next[{num_, fList_, lastP_, {p_, k_}}] := Module[{nP, f1List, p1, k1}, nP=NextPrime[First[Last[fList]]]; If[nP{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]]

Formula

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