A051178 Numbers k such that k divides the number of divisors of k!.
1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36, 40, 42, 45, 48, 52, 54, 56, 60, 64, 66, 70, 72, 76, 78, 80, 82, 84, 90, 96, 100, 102, 105, 108, 110, 112, 114, 120, 125, 126, 128, 130, 132, 135, 136, 140, 144, 150, 152, 156, 160, 162, 168
Offset: 1
Examples
6 is a term because the number of divisors of 6! is 30, which is divisible by 6.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Programs
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Haskell
a051178 n = a051178_list !! (n-1) a051178_list = filter (\x -> a027423 x `mod` x == 0) [1..] -- Reinhard Zumkeller, Feb 27 2013
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Mathematica
ok[n_] := Divisible[ DivisorSigma[0, n!], n]; Select[ Range[200], ok] (* Jean-François Alcover, Dec 08 2011 *) Select[Range[200],Mod[DivisorSigma[0,#!],#]==0&] (* Harvey P. Dale, Mar 13 2023 *)
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PARI
valp(n,p)=my(s); while(n\=p, s+=n); s is(n)=my(s=1); forprime(p=2,n, s*=valp(n,p)+1; s%=n; if(s==0, return(1))); n==1 \\ Charles R Greathouse IV, Nov 04 2016
Formula
It seems that a(n) is asymptotic to c*n with c=3.2..... - Benoit Cloitre, Sep 03 2002
A027423(a(n)) mod a(n) = 0. - Reinhard Zumkeller, Feb 27 2013
No member > 2 is prime. - Charlie Neder, Dec 23 2018
Comments