A229253 Total number of elements of nonempty subsets of divisors of n.

1, 4, 4, 12, 4, 32, 4, 32, 12, 32, 4, 192, 4, 32, 32, 80, 4, 192, 4, 192, 32, 32, 4, 1024, 12, 32, 32, 192, 4, 1024, 4, 192, 32, 32, 32, 2304, 4, 32, 32, 1024, 4, 1024, 4, 192, 192, 32, 4, 5120, 12, 192, 32, 192, 4, 1024, 32, 1024, 32, 32, 4, 24576, 4, 32, 192

Offset: 1

Author

Jaroslav Krizek, Sep 29 2013

Keywords

• nonn
• easy

Comments

Number of nonempty subsets of divisors of n = A100587(n).

Examples

			For n = 4; divisors of 4: {1, 2, 4}; nonempty subsets of divisors of n: {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; total number  of elements of subsets = 1 + 1 + 1 + 2 + 2 + 2 + 3 = 12.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000337, A001787, A003506, A100587.

Programs

Maple

with(numtheory): A229253:=n->tau(n)*2^(tau(n)-1): seq(A229253(n), n=1..100); # Wesley Ivan Hurt, Dec 12 2015

Mathematica

Table[Length[Flatten[Subsets[Divisors[n]]]], {n, 100}] (* T. D. Noe, Oct 01 2013 *)

PARI

A229253(n) = numdiv(n) * 2^(numdiv(n)-1); \\ Antti Karttunen, May 25 2017

Formula

a(n) = A001787(A000005(n)) = A000005(n) * 2^(A000005(n)-1) = A100587(n) + A000337(n-1) = tau(n) * 2^(tau(n)-1).