

A051178


Numbers k such that k divides number of divisors of k!.


3



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
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OFFSET

1,2


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)


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


EXAMPLE

6 is a term because the number of divisors of 6! is 30, which is divisible by 6.


MATHEMATICA

ok[n_] := Divisible[ DivisorSigma[0, n!], n]; Select[ Range[200], ok] (* JeanFrançois Alcover, Dec 08 2011 *)


PROG

(Haskell)
a051178 n = a051178_list !! (n1)
a051178_list = filter (\x > a027423 x `mod` x == 0) [1..]
 Reinhard Zumkeller, Feb 27 2013
(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


CROSSREFS

Cf. A000005, A000142, A027423, A277166.
Sequence in context: A097379 A114871 A085150 * A093891 A213708 A239063
Adjacent sequences: A051175 A051176 A051177 * A051179 A051180 A051181


KEYWORD

nonn,nice


AUTHOR

Leroy Quet


STATUS

approved



