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.

3, 5, 7, 8, 10, 10, 11, 12, 12, 14, 14, 13, 16, 14, 14, 14, 16, 16, 14, 20, 16, 18, 16, 20, 18, 17, 16, 16, 20, 18, 20, 20, 16, 20, 18, 20, 16, 16, 20, 14, 22, 26, 22, 18, 21, 24, 22, 20, 16, 20, 20, 28, 26, 26, 17, 20, 22, 26, 16, 24, 14, 18, 24, 24, 20, 14, 22, 26, 16, 24, 20

Offset

1,1

Comments

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

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(A006093(n)) + A000005(A008864(n)). - R. J. Mathar, Mar 03 2010

Maple

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

Mathematica

Table[p = Prime[n]; DivisorSigma[0, p - 1] + DivisorSigma[0, p + 1], {n, 100}]
Total[DivisorSigma[0, {#-1, #+1}]]&/@Prime[Range[80]] (* Harvey P. Dale, Feb 25 2012 *)

Prog

(PARI) a(n) = numdiv(prime(n)-1) + numdiv(prime(n)+1); \\ Amiram Eldar, Apr 17 2024
(PARI) lista(pmax) = forprime(p = 1, pmax, print1(numdiv(p-1) + numdiv(p+1), ", ")); \\ Amiram Eldar, Apr 17 2024

Crossrefs

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

Sequence in context: A120212 A093670 A185011 * A183054 A188569 A274140

Adjacent sequences: A175141 A175142 A175143 * A175145 A175146 A175147

Keyword

nonn,changed

Author

Leroy Quet, Feb 24 2010

Extensions

More terms from R. J. Mathar, Mar 03 2010

Status

approved