This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A141197 #20 Aug 29 2017 22:53:30 %S A141197 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, %T A141197 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, %U A141197 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 %N A141197 a(n) = the number of divisors of n that are each one less than a power of a prime. %C A141197 A067513(n) <= a(n) <= A000005(n). [From _Reinhard Zumkeller_, Oct 06 2008] %C A141197 a(A185208(n)) = 1. - _Reinhard Zumkeller_, Nov 01 2012 %H A141197 Reinhard Zumkeller, <a href="/A141197/b141197.txt">Table of n, a(n) for n = 1..10000</a> %F A141197 a(n) = sum (A010055(A027750(n,k)): k=1..A000005(n)). - _Reinhard Zumkeller_, Nov 01 2012 %e A141197 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. %t A141197 a[n_] := Select[Divisors[n], PrimeNu[# + 1] == 1 &] // Length; Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Aug 17 2013 *) %t A141197 Table[DivisorSum[n, 1 &, PrimePowerQ[# + 1] &], {n, 103}] (* _Michael De Vlieger_, Aug 29 2017 *) %o A141197 (Haskell) %o A141197 a141197 = sum . map (a010055 . (+ 1)) . a027750_row %o A141197 -- _Reinhard Zumkeller_, Nov 01 2012 %Y A141197 Cf. A141198. %Y A141197 Cf. A049073. %K A141197 nonn %O A141197 1,2 %A A141197 _Leroy Quet_, Jun 12 2008 %E A141197 Added more terms. - Steven Bi (chenhsi(AT)stanford.edu), Dec 22 2008 %E A141197 Added more terms (Terms 27 - 50). Steven Bi (chenhsi(AT)stanford.edu), Jan 09 2009 %E A141197 Corrected and extended by _Ray Chandler_, Jun 25 2009