A308530 -id:A308530 - cp's OEIS frontend

A308531 Largely composite numbers (A067128) with a unique number of divisors.

1, 4, 36, 48, 180, 720, 5040, 20160, 25200, 45360, 50400, 498960, 665280, 3603600, 6486480, 7207200, 8648640, 14414400, 32432400, 110270160, 698377680, 2095133040, 2205403200, 41902660800, 73329656400, 146659312800, 240940299600, 293318625600, 963761198400

Offset: 1

Amiram Eldar, Jun 06 2019

nonn

These are highly composite numbers (A002182) that have no other largely composite numbers with the same number of divisors.

The corresponding numbers of divisors d(a(n)) are 1, 3, 9, 10, 18, 30, 60, 84, 90, 100, ... (see the link for more values).

			4 is in the sequence since it is the only largely composite number with 3 divisors.
2 is not in the sequence since it has 2 divisors, the same as the next largely composite number 3.

Amiram Eldar, Table of n, a(n) for n = 1..114
Amiram Eldar, Table of n, a(n), d(a(n)) for n = 1..114

Cf. A000005, A002182, A067128, A308530.

s = {}; dm = 1; c = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c == 1, AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^8}]; s

A002182(k) is in the sequence if A308530(k) = 1.

A308532 Highly composite numbers (A002182) with a record number of largely composite numbers (A067128) having the same number of divisors.

Original entry on oeis.org

1, 2, 6, 60, 360, 73513440, 1396755360, 4497552259200, 130429015516800, 149602080797769600, 4488062423933088000, 6133685312708553600, 184010559381256608000, 7912454053394034144000, 19709923047004539052704000, 1162885459773267804109536000, 780296143507862696557498656000

Offset: 1

Amiram Eldar, Jun 06 2019

nonn

The corresponding record numbers of divisors d(a(n)) are 1, 2, 3, 6, 9, 10, 11, 14, 16, 20, ... (see the link for more values).

			6 is in the sequence since there are a record number of 3 largely composite numbers, 6, 8, and 10 with the same number of divisors. The next record is of 60, with 6 largely composite numbers, 60, 72, 84, 90, 96, and 108, with the same number of divisors.

Amiram Eldar, Table of n, a(n) for n = 1..25
Amiram Eldar, Table of n, a(n), d(a(n)) for n = 1..25

Cf. A000005, A002182, A067128, A308530.

s = {}; dm = 1; c = 0; cm = 0; nprev = 1; Do[d = DivisorSigma[0, n]; If[d == dm, c++]; If[d > dm, dm = d; If[c > cm, cm = c; AppendTo[s, nprev]]; c = 1; nprev = n], {n, 1, 10^3}]; s

cp's OEIS Frontend

A308531 Largely composite numbers (A067128) with a unique number of divisors.

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