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A067399 Number of divisors of n in OR-numbral arithmetic. 10
1, 2, 2, 3, 2, 4, 3, 4, 2, 4, 2, 6, 2, 6, 5, 5, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 9, 2, 10, 8, 6, 2, 4, 2, 6, 2, 4, 2, 8, 2, 6, 2, 6, 4, 4, 4, 10, 2, 4, 4, 6, 2, 8, 4, 12, 2, 4, 4, 15, 4, 16, 14, 7, 2, 4, 2, 6, 2, 4, 2, 8, 3, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 9, 5, 4, 2, 8, 2, 8, 4, 6, 2, 8, 6, 12, 2, 4, 4, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A048888 for the definition of OR-numbral arithmetic. The example shows that this sequence is not multiplicative.

In other words, number of lunar divisors of n in base 2.

REFERENCES

A. Frosini and S. Rinaldi, On the Sequence A079500 and Its Combinatorial Interpretations, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.1.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..1024

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.

Index entries for sequences related to dismal (or lunar) arithmetic

EXAMPLE

a(15)=5 since [15] has the 5 OR-numbral divisors [1], [3], [5], [7] and [15].

If written as a triangle with rows of lengths 1,2,4,8,16,...:

1,

2, 2,

3, 2, 4, 3,

4, 2, 4, 2, 6, 2, 6, 5,

5, 2, 4, 2, 6, 3, 4, 2, 8, 2, 4, 4, 9, 2, 10, 8,

6, 2, 4, 2, 6, 2, 4, 2, 8, 2, 6, 2, 6, 4, 4, 4, 10, 2, 4, 4, 6, 2, 8, 4, 12, 2, 4, 4, 15, 4, 16, 14,

...,

the last terms in each row give A079500(n). The penultimate terms in the rows give 2*A079500(n-1). - N. J. A. Sloane, Mar 05 2011

CROSSREFS

A079500 is the subsequence a(2^k-1). - N. J. A. Sloane, Feb 23 2011

Cf. A003986, A007059, A048888, A067138, A067139, A067398, A067400, A067401.

See A188548 for the sum of the divisors.

Sequence in context: A205000 A066241 A060025 * A106737 A323164 A318881

Adjacent sequences:  A067396 A067397 A067398 * A067400 A067401 A067402

KEYWORD

nonn

AUTHOR

Jens Voß, Jan 23 2002

STATUS

approved

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Last modified January 19 15:53 EST 2019. Contains 319307 sequences. (Running on oeis4.)