A378631 Numbers that set records in A377071.

1, 6, 12, 24, 30, 60, 120, 210, 420, 840, 1680, 2310, 3360, 4620, 6720, 9240, 18480, 36960, 60060, 73920, 120120, 147840, 240240, 480480, 960960, 1921920, 3843840, 7687680, 8168160, 15375360, 16336320, 30750720, 32672640, 65345280, 130690560, 261381120, 310390080

Offset: 1

Author

Michael De Vlieger, Dec 02 2024

Keywords

• nonn
• easy

Comments

Numbers n that set records for binomial(bigomega(n)+omega(n)-1, omega(n)-1), where bigomega = A001222 and omega = A001221.

a(n) is of the form 2^k * P(i), k >= 0, where primorial P = A002110.

Proper subset of A070175.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A001221, A001222, A002110, A007947, A070175, A377071.

Programs

Mathematica

f[x_] := Block[{i, k, m, nn, p}, nn = Product[Prime[j], {j, x}]; Set[{k, i, p}, Range[0, 2]]; {1}~Join~Union@ Reap[Until[i > x, While[Set[m, 2^k*p] <= nn, Sow[m]; k++]; k = 0; i++; p *= Prime[i] ] ][[-1, 1]] ] (* generate A070175 *);
r = 0; Reap[Do[If[# > r, r = #; Sow[n]] &@ Binomial[#2 + #1 - 1, #1 - 1] & @@ {PrimeNu[n], PrimeOmega[n]}, {n, f[10]}] ][[-1, 1]]