A379164 Achilles numbers that are deficient.

675, 1125, 1323, 2312, 2888, 3087, 3267, 4232, 4563, 5324, 6075, 6125, 6728, 7688, 7803, 8575, 8788, 9747, 10125, 10952, 11907, 11979, 13448, 14283, 14792, 15125, 16875, 17672, 19652, 19773, 21125, 22472, 22707, 25947, 27436, 27783, 27848, 28125, 29403, 29768, 30375, 33275, 35912, 36125, 36963, 40328

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

675=3^3*5^2 is a term because it is an Achilles number (powerful but imperfect, see A052486) and it is larger than the sum of its proper divisors (1+3+5+9+15+25+27+45+75+135+225=565).
1125=3^2*5^3 is a term because it is an Achilles number (powerful but imperfect, see A052486) and it is larger than the sum of its proper divisors (1+3+5+9+15+25+45+75+125+225+ 375=903).

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[42000], q] (* Amiram Eldar, Dec 17 2024 *)

Crossrefs

Intersection of A005100 and A052486.

Cf. A378859.

Sequence in context: A267818 A158392 A264328 * A124942 A158393 A294949

Adjacent sequences: A379161 A379162 A379163 * A379165 A379166 A379167

Keyword

nonn

Author

Massimo Kofler, Dec 17 2024

Status

approved