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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.
6
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.
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
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 24 2010
EXTENSIONS
More terms from R. J. Mathar, Mar 03 2010
STATUS
approved