A051178 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This sequence is not closed under multiplication. For example, 2*52=104 and 2*82=164 are not terms. - Ivan N. Ianakiev, Jan 23 2023

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] (* Jean-François Alcover, Dec 08 2011 *)

Select[Range[200], Mod[DivisorSigma[0, #!], #]==0&] (* Harvey P. Dale, Mar 13 2023 *)

PROG

(Haskell)

a051178 n = a051178_list !! (n-1)

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: A371288 A114871 A085150 * A093891 A213708 A371176

Adjacent sequences: A051175 A051176 A051177 * A051179 A051180 A051181

KEYWORD

nonn,nice

AUTHOR

Leroy Quet

STATUS

approved