A378630 Numbers that set records in A376567.

1, 2, 4, 6, 12, 24, 30, 48, 60, 120, 210, 240, 420, 840, 1680, 3360, 6720, 9240, 13440, 18480, 26880, 36960, 73920, 147840, 240240, 295680, 480480, 591360, 960960, 1921920, 3843840, 7687680, 15375360, 30750720, 32672640, 61501440, 65345280, 123002880, 130690560

Offset

1,2

Comments

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

Crossrefs

Cf. A000079, A001221, A001222, A002110, A007947, A070175, A376567.

Sequence in context: A362081 A265719 A380146 * A126098 A018894 A340816

Adjacent sequences: A378627 A378628 A378629 * A378631 A378632 A378633

Keyword

nonn,easy

Author

Michael De Vlieger, Dec 02 2024

Status

approved