OFFSET
1,2
COMMENTS
Where record values of Sum_{d|n} 1/tau(d) occur.
Terms a(n) are the smallest number from sequences numbers with following prime signatures: {}, {1}, {2}, {1, 1}, {2, 1}, {3, 1}, {1, 1, 1}, {4, 1}, {2, 1, 1}, {3, 1, 1}, {2, 2, 1}, {1, 1, 1, 1}, {4, 1, 1}, {3, 2, 1}, ...
EXAMPLE
For n = 4; a(4) = 6 because 6 is the smallest number such that Sum_{d|a(4)} 1/tau(d) = Sum_{d|6} 1/tau(d) = 9/4 > Sum_{d|a(3)} 1/tau(d) = Sum_{d|4} 1/tau(d) = 11/6.
PROG
(Magma) a:=1; S:=[a]; for n in [2..25] do k:=0; flag:= true; while flag do k+:=1; if &+[1/NumberOfDivisors(d): d in Divisors(a)] lt &+[1/NumberOfDivisors(d): d in Divisors(k)] then Append(~S, k); a:=k; flag:=false; end if; end while; end for; S;
(PARI) lista(nn) = {m = 0; for (n=1, nn, if ((mm = sumdiv(n, d, 1/numdiv(d))) > m, print1(n, ", "); m = mm); ); } \\ Michel Marcus, Dec 22 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Dec 14 2015
EXTENSIONS
More terms from Michel Marcus, Dec 22 2015
STATUS
approved