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A284149 a(n) = smallest number whose arithmetic derivative has exactly n prime factors. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A248930

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

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Last modified November 16 22:43 EST 2018. Contains 317275 sequences. (Running on oeis4.)