A141197 a(n) = the number of divisors of n that are each one less than a power of a prime.
1, 2, 2, 3, 1, 4, 2, 4, 2, 3, 1, 6, 1, 3, 3, 5, 1, 5, 1, 4, 3, 3, 1, 8, 1, 3, 2, 5, 1, 7, 2, 5, 2, 2, 2, 8, 1, 2, 2, 6, 1, 6, 1, 4, 3, 3, 1, 10, 2, 3, 2, 5, 1, 5, 1, 6, 2, 3, 1, 10, 1, 3, 4, 5, 1, 6, 1, 3, 2, 5, 1, 11, 1, 2, 3, 3, 2, 6, 1, 8, 2, 3, 1, 9, 1, 2, 2, 6, 1, 8, 2, 4, 3, 2, 1, 11, 1, 3, 2, 5, 1, 5, 1
Offset: 1
Keywords
Examples
The divisors of 9 are 1,3,9. 1 is one less than 2, a power of a prime. 3 is one less than 4, a power of a prime. And 9 is one less than 10, not a power of a prime. There are therefore 2 such divisors that are each one less than a power of a prime. So a(9)=2.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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Haskell
a141197 = sum . map (a010055 . (+ 1)) . a027750_row -- Reinhard Zumkeller, Nov 01 2012
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Mathematica
a[n_] := Select[Divisors[n], PrimeNu[# + 1] == 1 &] // Length; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Aug 17 2013 *) Table[DivisorSum[n, 1 &, PrimePowerQ[# + 1] &], {n, 103}] (* Michael De Vlieger, Aug 29 2017 *)
Formula
Extensions
Added more terms. - Steven Bi (chenhsi(AT)stanford.edu), Dec 22 2008
Added more terms (Terms 27 - 50). Steven Bi (chenhsi(AT)stanford.edu), Jan 09 2009
Corrected and extended by Ray Chandler, Jun 25 2009
Comments