OFFSET
1,1
COMMENTS
Observation: digsum(k) = tau(k)*prime(n) is minimum if tau(k) = 2 => k prime.
So, a(n) is prime if n > 2 and contains a majority of digits "9". For n > 3, digsum(a(n)) = A100484(n) = 10, 14, 22, 26, 34, 38, 46, 58, 62, ... (even semiprimes).
EXAMPLE
a(6) = 1889 because tau(1889) = 2 and (1+8+8+9)/2 = 13 = prime(6).
MAPLE
with(numtheory):for n from 1 to 18 do: p:=ithprime(n):ii:=0:for k from 1 to 10^8 while(ii=0)do:x:=convert(k, base, 10):n1:=nops(x):s:=sum('x[j]', 'j'=1..n1):s:=s/tau(k):if s=p then printf ( "%d %d \n", n, k):ii:=1:else fi:od:od:
MATHEMATICA
lst={}; Do[k=1; While[Plus@@IntegerDigits[k]/DivisorSigma[0, k]!=Prime[n], k++]; Print[n, " ", k], {n, 1, 10}]
CROSSREFS
KEYWORD
nonn,base,hard
AUTHOR
Michel Lagneau, Apr 14 2014
STATUS
approved