A194230 Least k such that the sum of the distinct prime divisors of k equals m^n for some m > 1.

2, 14, 15, 39, 87, 183, 2071, 1255, 1527, 3063, 28546, 12279, 106327, 49143, 622231, 1113823, 1703767, 1310695, 9961111, 3145719, 29360002, 12582903, 218103418, 50331639, 2046816631, 335544295, 9932108986, 23890747663, 1610612727

Offset

1,1

Comments

The sequence A063869 gives the least k such that sigma(k)=m^n for some m>1.

In this sequence, except n=2 -> m=3, the program gives m = 2 for n = 1 to 30.

All terms are squarefree. [Charles R Greathouse IV, Aug 19 2011]

Links

Table of n, a(n) for n=1..29.

Formula

a(n)=Min{x : A008472 (x)= m^n} for some m.

Example

a(11) = 28546 because the sum of the distinct prime divisors {2, 7, 2039} is 2048 = 2^11.

Maple

with(numtheory):for n from 1 to 12 do:ii:=0:for k from 1 to 1000000 while(ii=0) do: ii:=0:x:=factorset(k):p1:=sum(x[i], i=1..nops(x)):jj:=0:for m from 2 to 10 while(jj=0) do :if p1=m^n then ii:=1:jj:=1: printf ( "%d %d \n", n, k):else fi:od:od:od:

Crossrefs

Cf. A008472 A063869.

Sequence in context: A009774 A276553 A032933 * A109993 A075041 A105453

Adjacent sequences: A194227 A194228 A194229 * A194231 A194232 A194233

Keyword

nonn

Author

Michel Lagneau, Aug 19 2011

Status

approved