A175144 - OEIS

%I #23 Apr 17 2024 02:34:15

%S 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 18,17,16,16,20,18,20,20,16,20,18,20,16,16,20,14,22,26,22,18,21,24,22,

%U 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 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 If a(n) is a record, then the n-th prime is in sequence A090481.

%H T. D. Noe, <a href="/A175144/b175144.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000005(A006093(n)) + A000005(A008864(n)). - _R. J. Mathar_, Mar 03 2010

%p 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 Table[p = Prime[n]; DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1], {n, 100}]

%t Total[DivisorSigma[0,{#-1,#+1}]]&/@Prime[Range[80]] (* _Harvey P. Dale_, Feb 25 2012 *)

%o (PARI) a(n) = numdiv(prime(n)-1) + numdiv(prime(n)+1); \\ _Amiram Eldar_, Apr 17 2024

%o (PARI) lista(pmax) = forprime(p = 1, pmax, print1(numdiv(p-1) + numdiv(p+1), ", ")); \\ _Amiram Eldar_, Apr 17 2024

%Y Cf. A000005, A006093, A008864, A090481, A090482, A175146.

%K nonn

%O 1,1

%A _Leroy Quet_, Feb 24 2010

%E More terms from _R. J. Mathar_, Mar 03 2010