A339010 a(n) is the number of ways to write n as the difference of two centered k-gonal numbers for k >= 3.
0, 0, 1, 1, 1, 2, 1, 2, 3, 2, 1, 5, 1, 2, 5, 3, 1, 6, 1, 5, 5, 2, 1, 8, 3, 2, 6, 5, 1, 10, 1, 4, 5, 2, 5, 12, 1, 2, 5, 8, 1, 10, 1, 5, 12, 2, 1, 11, 3, 6, 5, 5, 1, 12, 5, 8, 5, 2, 1, 19, 1, 2, 12, 5, 5, 10, 1, 5, 5, 10, 1, 18, 1, 2, 12, 5, 5, 10, 1, 11, 10, 2
Offset: 1
Keywords
Examples
For n = 35, the a(35) = 5 differences are: A101321( 5,4) - A101321( 5,2) = 51 - 16 = 35, A101321( 5,7) - A101321( 5,6) = 141 - 106 = 35, A101321( 7,3) - A101321( 7,1) = 43 - 8 = 35, A101321( 7,5) - A101321( 7,4) = 106 - 71 = 35, and A101321(36,1) - A101321(36,0) = 36 - 1 = 35.
Links
- Peter Kagey, Table of n, a(n) for n = 1..10000
- Code Golf Stack Exchange, Uncentered Polygons
- OEIS Wiki, Centered polygonal numbers
- Eric Weisstein's World of Mathematics, Centered Polygonal Number
- Wikipedia, Centered polygonal number
Crossrefs
Programs
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PARI
a(n) = sumdiv(n, d, if (3*d <= n, numdiv(d>>valuation(d, 2)))); \\ Michel Marcus, Nov 19 2020
Formula
a(n) = Sum_{d|n, 3*d <= n} A001227(d).
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