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A339939 Coreful weird numbers: numbers k that are coreful abundant (A308053) but no subset their aliquot coreful divisors sums to k. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Similar sequences: A006037, A064114, A292986, A306984, A321146, A327948.
Sequence in context: A251325 A186478 A220059 * A321146 A107545 A256363
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 23 2020
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)