A227419 Least k such that the sum of the semiprime divisors equals n times the sum of the prime divisors, or 0 if no such k exists.

4, 9, 90, 25, 300, 49, 735, 1770, 7644, 121, 2541, 169, 5187, 6710, 8463, 289, 10982, 361, 11913, 13202, 24339, 529, 18515, 19513, 37851, 20723, 43239, 841, 35322, 961, 43215, 20705, 146595, 270470, 110823, 1369, 62835, 46535, 632316, 1681, 106074, 1849

Offset

2,1

Comments

Least k such that A076290(k) = n*A008472(k), or 0 if no such k exists. a(n) = n^2 if n is a prime number => A001248 is a subsequence.

Conjecture: a(n) > 0.

Links

Donovan Johnson, Table of n, a(n) for n = 2..1000

Example

a(12) = 2541: The divisors of 2541 are {1, 3, 7, 11, 21, 33, 77, 121, 231, 363, 847, 2541}, so the sum of the semiprime divisors is 21 + 33 + 77 + 121 = 252, which is 12 times the sum of prime divisors 3 + 7 + 11 = 21.

Maple

with(numtheory):for n from 2 to 43 do:ii:=0:for k from 2 to 700000 while(ii=0) do:x:=divisors(k):n1:=nops(x): y:=factorset(k):n2:=nops(y):s1:=0:s2:=0:for i from 1 to n1 do: if bigomega(x[i])=2 then s1:=s1+x[i]:else fi:od: s2:=sum('y[i]', 'i'=1..n2):if s1=n*s2 then ii:=1: printf ( "%d %d \n", n, k):else fi:od:od:

Crossrefs

Cf. A001248, A076290, A008472.

Sequence in context: A368629 A077530 A115551 * A242097 A220972 A335088

Adjacent sequences: A227416 A227417 A227418 * A227420 A227421 A227422

Keyword

nonn

Author

Michel Lagneau, Jul 18 2013

Status

approved