A275449 Least odd primitive abundant number with n prime factors, counted with multiplicity.

945, 7425, 81081, 78975, 1468935, 6375105, 85930875, 307879299, 1519691625, 8853249375, 17062700625, 535868474337, 2241870572475, 12759034818375, 64260996890625, 866566808687853, 2964430488515625, 23849823423763953, 100139192108634825, 772934641006640625, 2696807941801171875

Offset

5,1

Comments

See A188342 = (945, 3465, 15015, 692835, 22309287, ...) for the least odd primitive abundant number (A006038) with n distinct prime factors.

At least up to a(11), the greatest prime factor gpf(a(n)) = Q(a(n)/gpf(a(n))), where Q(N) = floor(sigma(N)/(2N-sigma(N))). In general one has to apply the precprime() function A007917 to this integer.

The above holds also for a(12)-a(15). Lars Blomberg, Apr 09 2018

Links

Table of n, a(n) for n=5..25.

Example

We have:   a(5) = 945 = 3^3 * 5   * 7,
          a(6) = 7425 = 3^3 * 5^2 * 11,
         a(7) = 81081 = 3^4 *  7  * 11 * 13,
        a(8) =  78975 = 3^5 * 5^2 * 13,
       a(9) = 1468935 = 3^6 * 5   * 13 * 31,
      a(10) = 6375105 = 3^7 * 5   * 11 * 53,
     a(11) = 85930875 = 3^6 * 5^3 * 23 * 41,
    a(12) = 307879299 = 3^7 * 7^2 * 13^2 * 17,
   a(13) = 1519691625 = 3^8 * 5^3 * 17 * 109,
   a(14) = 8853249375 = 3^8 * 5^4 * 17 * 127,
  a(15) = 17062700625 = 3^9 * 5^4 * 19 * 73.

Prog

(PARI) a(n)=for(i=1, #A=A006038, bigomega(A[i])==n&&return(A[i])) \\ Provided that A006038 is defined as a set with enough elements. - M. F. Hasler, Jul 27 2016
(PARI)
generate(A, B, n) = A=max(A, 3^n); (f(m, p, k) = my(list=List()); if(sigma(m) > 2*m, return(list)); if(k==1, forprime(q=max(p, ceil(A/m)), B\m, my(t=m*q); if(sigma(t) > 2*t, my(F=factor(t)[, 1], ok=1); for(i=1, #F, if(sigma(t\F[i], -1) > 2, ok=0; break)); if(ok, listput(list, t)))), forprime(q = p, sqrtnint(B\m, k), list=concat(list, f(m*q, q, k-1)))); list); vecsort(Vec(f(1, 3, n)));
a(n) = my(x=3^n, y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ Daniel Suteu, Feb 10 2024

Crossrefs

Cf. A006038, A188342, A188439.

Sequence in context: A188342 A109729 A294025 * A293186 A294027 A127666

Adjacent sequences: A275446 A275447 A275448 * A275450 A275451 A275452

Keyword

nonn

Author

M. F. Hasler, Jul 27 2016

Extensions

a(12)-a(15) from Lars Blomberg, Apr 09 2018

a(16)-a(25) from Daniel Suteu, Feb 10 2024

Status

approved