A348342 Noninfinitary highly composite numbers: where the number of noninfinitary divisors (A348341) increases to a record.

1, 4, 12, 16, 36, 48, 144, 240, 576, 720, 1680, 2880, 3600, 5040, 11520, 14400, 15120, 20160, 25200, 45360, 55440, 80640, 100800, 166320, 176400, 226800, 277200, 498960, 720720, 887040, 1108800, 1587600, 1940400, 2494800, 3603600, 6486480, 9979200, 11531520, 14414400

Offset

1,2

Comments

The record numbers of noninfinitary divisors are 0, 1, 2, 3, 5, 6, 11, 12, 13, 22, 24, 26, 37, 44, 46, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..468

Amiram Eldar, Table of n, a(n), A348341(a(n)) for n = 1..468

Mathematica

nid[1] = 0; nid[n_] := DivisorSigma[0, n] - Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[;; , 2]]]; dm = -1; s = {}; Do[If[(d = nid[n]) > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s

Crossrefs

Cf. A348341.

Subsequence of A025487.

Similar sequences: A002182, A002110 (unitary), A037992 (infinitary), A293185, A306736, A307845, A309141, A318278, A322484, A335386.

Sequence in context: A353793 A273501 A291781 * A348273 A374905 A253122

Adjacent sequences: A348339 A348340 A348341 * A348343 A348344 A348345

Keyword

nonn

Author

Amiram Eldar, Oct 13 2021

Status

approved