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

Author

Hal M. Switkay, Dec 11 2022

Keywords

• nonn

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).

Crossrefs

Cf. A000005, A000203, A210594.

Programs

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 *)

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

Extensions

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

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