A140645 Digit sums of highly composite numbers.

1, 2, 4, 6, 3, 6, 9, 12, 6, 3, 9, 6, 9, 9, 12, 9, 15, 9, 9, 18, 9, 9, 9, 9, 18, 18, 9, 18, 18, 18, 18, 18, 18, 18, 36, 18, 27, 18, 18, 18, 18

Offset: 1

Author

Parthasarathy Nambi, Jul 08 2008

Keywords

• nonn
• base

Comments

Except for the first three terms, all others are multiples of 3.

Examples

			2162160 is a highly composite number whose digit sum is 18.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Achim Flammenkamp, Table of 1200 Highly Composite Numbers.
• Graeme McRae, Highly Composite Numbers.

Crossrefs

Cf. A002182, A002183, A007953, A117825, A127390.

Programs

Mathematica

HCN=NestList[Function[last,Module[{d = DivisorSigma[0, last]},NestWhile[# + 1 &, last, DivisorSigma[0, #] <= d &]]], 1,40]; DigitSum/@HCN (* James C. McMahon, Jul 12 2025 *)

Formula

a(n) = A007953(A002182(n)). - Amiram Eldar, Nov 13 2019