A378814 a(n) = round(n/(A000005(A071904(n))-2)).

1, 1, 2, 4, 3, 3, 4, 4, 2, 10, 6, 6, 7, 4, 8, 8, 4, 9, 6, 10, 11, 11, 12, 12, 6, 4, 14, 14, 7, 15, 31, 16, 17, 17, 18, 6, 19, 19, 20, 10, 10, 21, 22, 22, 8, 46, 12, 12, 25, 25, 26, 26, 9, 9, 28, 28, 29, 15, 30, 30, 31, 31, 32, 32, 9, 11, 34, 34, 17, 18, 36

Offset: 1

Author

Bill McEachen, Dec 08 2024

Keywords

• nonn

Comments

Nearly all of the data falls on lines discussed below. There are a few "outliers" visible on the graph. There are <120 such outliers in the first 20000 terms (about 0.6%). Many of the outlier indices belong to A037040. The lines are n, (n+0)/2, (n+2)/4, (n+4)/6, (n+6)/8,....

Examples

			Let n=14, A071904(n)=63, tau(63)=6 so a(14)=round(14/(6-2))=4.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Bill McEachen, Plot 20K terms
• Bill McEachen, A037040 overlap (TEMP)

Crossrefs

Cf. A000005, A037040, A071904.

Programs

Mathematica

MapIndexed[Floor[#2[[1]]/# + 1/2] &, DivisorSigma[0, Select[Range[9, 500, 2], CompositeQ]] - 2] (* Paolo Xausa, Dec 16 2024 *)