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A275449 Least odd primitive abundant number with n prime factors, counted with multiplicity. 2
945, 7425, 81081, 78975, 1468935, 6375105, 85930875, 307879299, 1519691625, 8853249375, 17062700625 (list; graph; refs; listen; history; text; internal format)
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..15.

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

CROSSREFS

Cf. A006038, A188342, A188439.

Sequence in context: A188342 A109729 A294025 * A293186 A294027 A127666

Adjacent sequences:  A275446 A275447 A275448 * A275450 A275451 A275452

KEYWORD

nonn,more

AUTHOR

M. F. Hasler, Jul 27 2016

EXTENSIONS

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

STATUS

approved

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Last modified April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)