A145337 -id:A145337 - cp's OEIS frontend

A145338 a(n) is the smallest prime p where |d(p-1) - d(p+1)| = n. (d(m) = the number of divisors of m.)

7, 2, 11, 197, 23, 37, 47, 401, 59, 1601, 181, 16901, 167, 3137, 179, 577, 419, 1297, 1051, 12101, 359, 739601, 1009, 4357, 1511, 50177, 719, 171610001, 839, 67601, 10657, 9096257, 1439, 240101, 3697, 145540097, 3023, 15877, 2879, 3587237, 2521

Offset: 0

Leroy Quet, Oct 08 2008

nonn

a(2n-1) = k^2 + 1, for all positive integers n, where k is some integer; k is even for n >= 2.

			a(2)=11 because abs(d(10) - d(12)) = 2 while abs(d(p-1) - d(p+1)) < 2 for p=2,3,5 and 7. - _Emeric Deutsch_, Oct 11 2008

Cf. A145337.

with(numtheory); a:=proc(n) local j: for j while abs(tau(ithprime(j)-1)-tau(ithprime(j)+1)) <> n do end do: ithprime(j) end proc: seq(a(n), n=0..26); # Emeric Deutsch, Oct 11 2008

More terms from R. J. Mathar and Emeric Deutsch, Oct 10 2008

Extended from a(27) onwards by Ray Chandler, Oct 12 2008

A190821 Prime numbers p where d(p-1) = d(p+1) increases to a record.

Original entry on oeis.org

7, 19, 41, 199, 919, 5741, 18089, 41651, 90271, 446081, 1276001, 27033161, 43220449, 53308529, 109245401, 512669249, 663929729, 2266639649, 2560742911, 2969200961, 8505402751, 32540473601, 61573368401, 74335064959, 109494811999

Offset: 1

Juri-Stepan Gerasimov, May 21 2011

nonn

a(26) <= 354208192001. - Donovan Johnson, Jun 03 2011

			a(1) = 7 because 7 is prime and d(6) = 4 = d(8).

Cf. A145337, A190646 (numbers n such that d(n-1)=d(n+1) increases to a record).

s = Select[Prime@ Range@ 1000000, DivisorSigma[0, # - 1] == DivisorSigma[0, # + 1] &]; t = DivisorSigma[0, # - 1] & /@ s; a = {0}; b = {0}; Do[If[t[[k]] > Max@ b, AppendTo[a, s[[k]]]]; AppendTo[b, t[[k]]], {k, Length@ s}]; a (* Michael De Vlieger, Oct 30 2015 *)

r=0; forprime(p=2,4e9,t=numdiv(p-1);if(t>r&t==numdiv(p+1),r=t; print1(p", "))) \\ Charles R Greathouse IV, May 27 2011

a(14)-a(21) from Charles R Greathouse IV, May 27 2011
a(22) from Charles R Greathouse IV, May 31 2011
a(23)-a(25) from Donovan Johnson, Jun 03 2011

cp's OEIS Frontend

A145338 a(n) is the smallest prime p where |d(p-1) - d(p+1)| = n. (d(m) = the number of divisors of m.)

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