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A229253
Total number of elements of nonempty subsets of divisors of n.
1
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
1,2
COMMENTS
Number of nonempty subsets of divisors of n = A100587(n).
LINKS
FORMULA
a(n) = A001787(A000005(n)) = A000005(n) * 2^(A000005(n)-1) = A100587(n) + A000337(n-1) = tau(n) * 2^(tau(n)-1).
EXAMPLE
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.
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 *)
PROG
(PARI) A229253(n) = numdiv(n) * 2^(numdiv(n)-1); \\ Antti Karttunen, May 25 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Sep 29 2013
STATUS
approved