A284149 a(n) = smallest number whose arithmetic derivative has exactly n prime factors.

6, 4, 8, 12, 16, 92, 64, 144, 508, 256, 1024, 3392, 8192, 3072, 13248, 19456, 114688, 81920, 65536, 262144, 671744, 1048576, 983040, 1835008, 5296128, 9437184, 16777216, 54525952, 121634816, 201326592, 587202560, 738197504, 3340500992, 6710886400, 3959422976, 4294967296, 28991029248, 18253611008, 68719476736

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Example

a(1) = 6 because 6' = 5;
a(2) = 4 because 4' = 4 = 2 * 2;
a(3) = 8 because 8' = 12 = 2 * 2 * 3.

Maple

with(numtheory): P:= proc(q) local k, n; for n from 1 to q do for k from 1 to q do
if bigomega(k*add(op(2, p)/op(1, p), p=ifactors(k)[2]))=n then print(k); break; fi;
od; od; end: P(10^9);

Mathematica

ad[1]=0; ad[n_] := n*Total[ (#1[[2]] / #1[[1]] &) /@ FactorInteger[n]]; a[n_] := Block[{k=2}, While[PrimeOmega@ ad[k] != n, k++]; k]; Array[a, 15] (* Giovanni Resta, Mar 22 2017 *)

Crossrefs

Cf. A003415.

Sequence in context: A195434 A199815 A155906 * A096499 A179258 A365937

Adjacent sequences: A284146 A284147 A284148 * A284150 A284151 A284152

Keyword

nonn

Author

Paolo P. Lava, Mar 21 2017

Extensions

a(29)-a(31) from Ray Chandler, Mar 24 2017

a(32)-a(33) from Hans Havermann, Mar 24 2017

a(34)-a(36) from Hans Havermann, Mar 26 2017

a(37)-a(39) from Hans Havermann, May 17 2017

Status

approved