%I #35 Feb 16 2020 20:44:18
%S 1,2,3,4,6,24,28,30,32,36,45,48,56,64,66,72,76,80,92,96,102,104,120,
%T 126,128,144,168,176,180,184,186,192,200,208,228,236,240,248,252,256,
%U 270,280,288,292,304,312,320,328,336,352,360,364,376,384,420,424,426
%N Numbers n such that d(prime(n)  1)  n, where d(k) is the number of divisors of k.
%C For n in {1,2,3,4,6}, n = d(prime(n)1). There are no others with this property, as conjectured by _Raphie Frank_ and proved by _Charles R Greathouse IV_ on Physics Forums (Nov, 2010).
%H T. D. Noe, <a href="/A217442/b217442.txt">Table of n, a(n) for n = 1..1000</a>
%H Physics Forums, <a href="http://www.physicsforums.com/showthread.php?t=442527">Prime Indices & the Divisors of (p'_n  1): A LatticeRelated Question</a> , Nov 2010
%e d(701  1)*7 = pi(701) = 126. The 126th prime is 701 and d(701  1) = 18; 18 divides 126 (7 times), so 126 is a member of this sequence.
%t Select[Range[352], Mod[#, DivisorSigma[0, Prime[#]  1]] == 0 &] (* _T. D. Noe_, Oct 11 2012 *)
%o (PARI) is(n)=n%numdiv(prime(n)1)==0 \\ _Charles R Greathouse IV_, Oct 09 2012
%Y Cf. A008328.
%K nonn
%O 1,2
%A _Raphie Frank_, Oct 04 2012
%E a(12), a(31), a(39) from _Charles R Greathouse IV_, Oct 09 2012
