A265719 Numbers n such that Sum_{d|n} 1/tau(d) > Sum_{d|m} 1/tau(d) for all m < n.

1, 2, 4, 6, 12, 24, 30, 48, 60, 120, 180, 210, 240, 360, 420, 720, 840, 1260, 1680, 2520, 4620, 5040, 7560, 9240, 13860, 18480, 27720, 55440, 83160, 110880, 120120, 166320, 180180, 240240, 360360, 720720, 1081080, 1441440, 1801800, 2042040, 2162160, 3063060, 3603600, 4084080

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}, ...

Links

Table of n, a(n) for n=1..44.

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

Cf. A000005, A237350, A253139, A265390, A265391, A265392, A265393.

Sequence in context: A097212 A266228 A362081 * A126098 A018894 A340816

Adjacent sequences: A265716 A265717 A265718 * A265720 A265721 A265722

Keyword

nonn

Author

Jaroslav Krizek, Dec 14 2015

Extensions

More terms from Michel Marcus, Dec 22 2015

Status

approved