A378632 Numbers that set records in A378181.

1, 4, 6, 12, 24, 48, 60, 96, 120, 240, 420, 480, 840, 1680, 3360, 6720, 13440, 18480, 26880, 36960, 53760, 73920, 147840, 295680, 480480, 591360, 960960, 1182720, 1921920, 3843840, 7687680, 15375360, 30750720, 61501440, 65345280, 123002880, 130690560, 246005760

Offset

1,2

Comments

Numbers n that set records for binomial(bigomega(n)+omega(n)-1, omega(n)), 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] & @@ {PrimeNu[n], PrimeOmega[n]}, {n, f[10]}] ][[-1, 1]]

Crossrefs

Cf. A000079, A001221, A001222, A002110, A007947, A070175, A378181.

Sequence in context: A357809 A162688 A362883 * A352634 A070232 A037100

Adjacent sequences: A378629 A378630 A378631 * A378633 A378634 A378636

Keyword

nonn,easy,new

Author

Michael De Vlieger, Dec 02 2024

Status

approved