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

1,2

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

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]]

Crossrefs

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

Sequence in context: A119500 A260633 A348632 * A365470 A110967 A000082

Adjacent sequences: A378626 A378629 A378630 * A378632 A378633 A378634

Keyword

nonn,easy,new

Author

Michael De Vlieger, Dec 02 2024

Status

approved