cp's OEIS Frontend

A175144 a(n) = d(p(n)-1) + d(p(n)+1), where p(n) is the n-th prime, and where d(m) is the number of divisors of m.

%I A175144 #23 Apr 17 2024 02:34:15
%S A175144 3,5,7,8,10,10,11,12,12,14,14,13,16,14,14,14,16,16,14,20,16,18,16,20,
%T A175144 18,17,16,16,20,18,20,20,16,20,18,20,16,16,20,14,22,26,22,18,21,24,22,
%U A175144 20,16,20,20,28,26,26,17,20,22,26,16,24,14,18,24,24,20,14,22,26,16,24,20
%N A175144 a(n) = d(p(n)-1) + d(p(n)+1), where p(n) is the n-th prime, and where d(m) is the number of divisors of m.
%C A175144 If a(n) is a record, then the n-th prime is in sequence A090481.
%H A175144 T. D. Noe, <a href="/A175144/b175144.txt">Table of n, a(n) for n = 1..10000</a>
%F A175144 a(n) = A000005(A006093(n)) + A000005(A008864(n)). - _R. J. Mathar_, Mar 03 2010
%p A175144 taudiff := proc(n) numtheory[tau](n-1)+numtheory[tau](n+1) ; end proc: A175144 := proc(n) taudiff(ithprime(n)) ; end proc: seq(A175144(n),n=1..80) ; # _R. J. Mathar_, Mar 03 2010
%t A175144 Table[p = Prime[n]; DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1], {n, 100}]
%t A175144 Total[DivisorSigma[0,{#-1,#+1}]]&/@Prime[Range[80]] (* _Harvey P. Dale_, Feb 25 2012 *)
%o A175144 (PARI) a(n) = numdiv(prime(n)-1) + numdiv(prime(n)+1); \\ _Amiram Eldar_, Apr 17 2024
%o A175144 (PARI) lista(pmax) = forprime(p = 1, pmax, print1(numdiv(p-1) + numdiv(p+1), ", ")); \\ _Amiram Eldar_, Apr 17 2024
%Y A175144 Cf. A000005, A006093, A008864, A090481, A090482, A175146.
%K A175144 nonn
%O A175144 1,1
%A A175144 _Leroy Quet_, Feb 24 2010
%E A175144 More terms from _R. J. Mathar_, Mar 03 2010