A339939 Coreful weird numbers: numbers k that are coreful abundant (A308053) but no subset their aliquot coreful divisors sums to k.

4900, 14700, 53900, 63700, 83300, 93100, 112700, 142100, 151900, 161700, 181300, 191100, 200900, 210700, 230300, 249900, 259700, 279300, 289100, 298900, 328300, 338100, 347900, 349448, 357700, 387100, 406700, 426300, 436100, 455700, 475300, 494900, 504700, 524300

Offset

1,1

Comments

First differs from A321146 at n = 24.

A coreful divisor d of a number k is a divisor with the same set of distinct prime factors as k, or rad(d) = rad(k), where rad(k) is the largest squarefree divisor of k (A007947).

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Example

4900 is a term since the sum of its aliquot coreful divisors, {70, 140, 350, 490, 700, 980, 2450}, is 5180 > 4900, and no subset of these divisors sums to 4900.

Mathematica

corDiv[n_] := Module[{rad = Times @@ FactorInteger [n][[;; , 1]]}, rad * Divisors[n/rad]]; corWeirdQ[n_] := Module[{d = Most@corDiv[n], x}, Plus @@ d > n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] == 0]; Select[Range[10^5], corWeirdQ]

Crossrefs

Subsequence of A308053.

Cf. A007947, A057723.

Similar sequences: A006037, A064114, A292986, A306984, A321146, A327948.

Sequence in context: A251325 A186478 A220059 * A321146 A374500 A107545

Adjacent sequences: A339936 A339937 A339938 * A339940 A339941 A339942

Keyword

nonn

Author

Amiram Eldar, Dec 23 2020

Status

approved