A192496 Smallest prime p such that there is a gap of sigma(n) between p and the next prime, otherwise 0.

2, 0, 7, 0, 23, 199, 89, 0, 0, 523, 199, 2971, 113, 1669, 1669, 0, 523, 0, 887, 16141, 5591, 9551, 1669, 43331, 0, 16141, 19333, 82073, 4297, 31397, 5591, 0, 28229, 35617, 28229, 0, 30593, 43331, 82073, 404851, 16141, 360653, 15683, 461717, 188029, 31397, 28229, 6752623, 0, 0, 31397

Offset

1,1

Comments

For n > 1, a(n)=0 if sigma(n) is odd. Sigma(n) is odd iff n is a square or twice a square. - Robert G. Wilson v, Oct 03 2001

Links

Antti Karttunen, Table of n, a(n) for n = 1..479 (prepared from the b-file of A000230 whose data is from Thomas R. Nicely's website)

Example

a(6) = 199  because 211 - 199 = 12 = sigma(6).

Maple

A000230 := proc(n) option remember; local i ; for i from 1 do if ithprime(i+1) -ithprime(i) = 2*n then return ithprime(i) ; end if; end do: end proc:
A192496 := proc(n) s := numtheory[sigma](n) ; if s = 1 then 2 ; elif type(s, 'odd') then 0; else A000230(s/2) ; end if; end proc:
for n from 1 do print(A192496(n)) ; end do: # R. J. Mathar, Jul 04 2011

Mathematica

With[{s = Differences@ Prime@ Range[10^6]}, Array[Prime@ FirstPosition[s, DivisorSigma[1, #]][[1]] /. k_ /; ! IntegerQ@ k -> 0 &, 51]] (* Michael De Vlieger, Nov 23 2017 *)

Crossrefs

Cf. A000203, A000230.

Sequence in context: A142709 A266220 A022897 * A156442 A268683 A174968

Adjacent sequences: A192493 A192494 A192495 * A192497 A192498 A192499

Keyword

nonn

Author

Michel Lagneau, Jul 02 2011

Extensions

Corrected by R. J. Mathar, Jul 04 2011

Status

approved