A378859 Achilles numbers that are abundant.

72, 108, 200, 288, 392, 432, 500, 648, 800, 864, 968, 972, 1152, 1352, 1372, 1568, 1800, 1944, 2000, 2592, 2700, 3200, 3456, 3528, 3872, 3888, 4000, 4500, 4608, 5000, 5292, 5400, 5408, 5488, 6272, 6912, 7200, 8712, 8748, 9000, 9248, 9800, 10368, 10584, 10800, 10976, 11552, 12168, 12348, 12500, 12800, 13068, 13500, 14112, 15488

Offset

1,1

Comments

33075 is the smaller odd term in a longer sequence.

Links

Table of n, a(n) for n=1..55.

Example

72=2^3*3^2 is a term because it is an Achilles number (powerful but imperfect, see A052486) and it is smaller than the sum of its proper divisors (1+2+3+4+6+8+9+12+18+24+36=123).
108=2^2*3^3 is a term because it is an Achilles number (powerful but imperfect, see A052486) and it is smaller than the sum of its proper divisors (1+2+3+4+6+9+12+18+27+36+54=172).

Mathematica

q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; AllTrue[e, # > 1 &] && GCD @@ e == 1 && Times @@ ((p - 1/p^e)/(p - 1)) > 2]; Select[Range[16000], q] (* Amiram Eldar, Dec 09 2024 *)

Crossrefs

Intersection of A005101 and A052486.

Sequence in context: A272191 A072412 A052486 * A114128 A375074 A375143

Adjacent sequences: A378852 A378853 A378858 * A378860 A378861 A378862

Keyword

nonn

Author

Massimo Kofler, Dec 09 2024

Status

approved