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 A217442 Numbers n such that d(prime(n) - 1) | n, where d(k) is the number of divisors of k. 1

%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 Lattice-Related 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

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Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)