A051178 -id:A051178 - cp's OEIS frontend

A277166 Numbers m such that m divides the number of divisors of m!!.

1, 2, 4, 8, 15, 16, 24, 27, 32, 36, 40, 48, 54, 56, 60, 63, 64, 72, 80, 84, 90, 96, 104, 105, 108, 112, 120, 128, 132, 135, 140, 144, 147, 152, 156, 160, 164, 165, 168, 180, 189, 192, 195, 200, 204, 210, 216, 220, 224, 225, 228, 231, 240, 243, 250, 252, 256

Offset: 1

Michel Lagneau, Oct 01 2016

nonn

It seems that a(n) is asymptotic to c*n with c = 4.8...

			8 is in the sequence because the number of divisor of 8!! is A114338(8) = 16, which is divisible by 8.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A006882, A051178, A114338.

ok[n_] := Divisible[ DivisorSigma[0, n!!], n]; Select[ Range[200], ok]

isok(n) = (numdiv(prod(i=0, (n-1)\2, n - 2*i)) % n) == 0; \\ after first Pari in A006882; Michel Marcus, Oct 02 2016

A114338(a(n)) mod a(n) = 0.

A275250 Odd numbers n that divide the number of divisors of n!.

Original entry on oeis.org

1, 27, 45, 105, 125, 135, 175, 189, 225, 231, 243, 297, 315, 351, 375, 385, 405, 441, 455, 495, 525, 539, 567, 585, 595, 605, 625, 637, 663, 675, 693, 715, 729, 735, 741, 765, 819, 825, 845, 847, 855, 875, 891, 935, 945, 969, 975, 1001, 1029, 1035, 1045, 1053, 1089

Offset: 1

Altug Alkan, Jul 21 2016

nonn

Odd terms of A051178.

			The odd number 27 is a term because A000005(27!) = 2^9*3^3*7^2 is divisible by 27.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A051178, A027423.

N:= 2000: # to get all terms <= N
P:= select(isprime, [2,seq(i,i=3..N,2)]):
d:= Vector(nops(P),1):
A:= 1:
for n from 2 to N do
  f:= ifactors(n)[2];
  for t in f do
    if member(t[1],P,'k') then
        d[k]:= d[k] + t[2]
    fi
  od:
  if n::odd and convert(d,`*`) mod n = 0 then A:= A, n fi;
od:
A; # Robert Israel, Aug 05 2016

A275250Q = OddQ[#] && Divisible[DivisorSigma[0, #!], #] &; Select[Range[500], A275250Q] (* JungHwan Min, Jul 29 2016 *)

isok(n) = (n % 2) && !(numdiv(n!) % n); \\ Michel Marcus, Jul 26 2016

cp's OEIS Frontend

A277166 Numbers m such that m divides the number of divisors of m!!.

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