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 A141198 #19 Jun 22 2025 11:39:05 %S A141198 0,1,1,2,1,3,0,3,2,3,0,5,0,2,2,3,1,5,0,5,1,1,0,7,1,2,2,4,0,6,0,4,2,2, %T A141198 1,7,0,2,1,6,0,5,0,3,3,1,0,8,0,4,2,3,0,6,1,5,1,1,0,10,0,2,2,4,2,4,0,4, %U A141198 1,4,0,10,0,2,2,3,0,4,0,7,2,2,0,9,2,1,1,4,0,9,0,2,1,1,1,9,0,3,3,6,0,5,0 %N A141198 a(n) is the number of divisors of n that are each one more than a power of a prime. %C A141198 1 is considered here to be a power of a prime. 0 is not considered here to be a power of a prime. %H A141198 Amiram Eldar, <a href="/A141198/b141198.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1049 from Diana Mecum) %e A141198 The divisors of 9 are 1, 3 and 9. 1 is one more than 0, not a power of a prime. 3 is one more than 2, a power of a prime. And 9 is one more than 8, a power of a prime. There are therefore 2 such divisors that are each one more than a power of a prime. So a(9) = 2. %t A141198 a[n_] := DivisorSum[n, 1 &, # == 2 || PrimePowerQ[#-1] &]; Array[a, 100] (* _Amiram Eldar_, Jun 22 2025 *) %o A141198 (PARI) a(n) = sumdiv(n, d, d == 2 || isprimepower(d - 1)); \\ _Amiram Eldar_, Jun 22 2025 %Y A141198 Cf. A000961, A141197. %K A141198 nonn %O A141198 1,4 %A A141198 _Leroy Quet_, Jun 12 2008 %E A141198 Corrected and extended by _Diana L. Mecum_, Jul 05 2007