A356573 Sigma-dense numbers: integers k such that sigma(k) * log(1+log(1+log(1+k))) / (k * log(1+log(1+k))) sets a new record.

1, 2, 4, 6, 12, 24, 60, 120, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 10810800, 21621600, 36756720, 61261200, 73513440, 122522400, 183783600

Offset

1,2

Comments

This sequence is to A210594 (the generalization in the latter's comment section) as sigma (A000203, the sum of divisors function) is to tau (A000005, the number of divisors function).

Links

Table of n, a(n) for n=1..38.

Mathematica

s={}; dm = 0; Do[If[(d = DivisorSigma[1, n] * Log[1 + Log[1 + Log[1 + n]]] / (n * Log[1 + Log[1 + n]])) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Dec 12 2022 *)

Prog

(PARI) listas(nn) = {my(m=0); for (k=1, nn, my(mm = sigma(k)*log(1+log(1+log(1+k))) / (k * log(1+log(1+k)))); if (mm > m, print1(k, ", "); m = mm); ); } \\ Michel Marcus, Dec 12 2022

Crossrefs

Cf. A000005, A000203, A210594.

Sequence in context: A058764 A087009 A168263 * A162936 A036484 A212654

Adjacent sequences: A356570 A356571 A356572 * A356574 A356575 A356576

Keyword

nonn

Author

Hal M. Switkay, Dec 11 2022

Extensions

a(22)-a(31) from Michel Marcus, Dec 12 2022

a(32)-a(38) from Amiram Eldar, Dec 12 2022

Status

approved