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A192496 Smallest prime p such that there is a gap of sigma(n) between p and the next prime, otherwise 0. 1
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 (list; graph; refs; listen; history; text; internal format)
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 T. 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

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Last modified July 2 08:50 EDT 2020. Contains 335398 sequences. (Running on oeis4.)