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A192498
Smallest prime p such that there is a gap of tau(n) between p and the next prime, otherwise 0.
1
2, 3, 3, 0, 3, 7, 3, 7, 0, 7, 3, 23, 3, 7, 7, 0, 3, 23, 3, 23, 7, 7, 3, 89, 0, 7, 7, 23, 3, 89, 3, 23, 7, 7, 7, 0, 3, 7, 7, 89, 3, 89, 3, 23, 23, 7, 3, 139, 0, 23, 7, 23, 3, 89, 7, 89, 7, 7, 3, 199, 3, 7, 23, 0, 7, 89, 3, 23, 7, 89, 3, 199, 3, 7, 23, 23, 7
OFFSET
1,1
COMMENTS
For n > 1, a(n)=0 if n is a perfect square (see A048691) because then tau(n) is odd.
LINKS
FORMULA
a(1) = 2; and for n > 1, if n = k^2, a(n) = 0, otherwise a(n) = A000230(A000005(n)/2). - Antti Karttunen, May 28 2017
EXAMPLE
a(12) = 23 because 29 - 23 = 6 = tau(12).
MAPLE
A000230 := proc(g) if g = 1 then return 2 ; elif type(g, 'odd') then return 0 ; else for i from 1 do if ithprime(i+1)-ithprime(i) = g then return ithprime(i) ; end if; end do: end if; end proc:
A192498 := proc(n) A000230(numtheory[tau](n)) ; end proc: # R. J. Mathar, Jul 12 2011
MATHEMATICA
Module[{nn=200, prs, dfs, thr}, prs=Prime[Range[nn]]; dfs=Differences[prs]; thr = DeleteDuplicatesBy[Thread[{Most[prs], dfs}], Last]; Join[{2}, Flatten[ Table[ Select[thr, #[[2]]==DivisorSigma[0, n]&], {n, 2, 80}]/.{}->{{0, 0}}, 1][[All, 1]]]] (* Harvey P. Dale, Mar 09 2021 *)
PROG
(PARI)
A000230(n) = { my(p=2); forprime(q=3, , if(q-p==2*n, return(p)); p=q); } \\ From Charles R Greathouse IV, Nov 20 2012
A192498(n) = if(1==n, 2, if(issquare(n), 0, A000230(numdiv(n)/2))); \\ Antti Karttunen, May 28 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 02 2011
STATUS
approved