login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
2
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 18 2013
STATUS
approved