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A308053 Coreful abundant numbers: numbers k such that csigma(k) > 2*k, where csigma(k) is the sum of the coreful divisors of k (A057723). 13
72, 108, 144, 200, 216, 288, 324, 360, 400, 432, 504, 540, 576, 600, 648, 720, 756, 784, 792, 800, 864, 900, 936, 972, 1000, 1008, 1080, 1152, 1188, 1200, 1224, 1296, 1368, 1400, 1404, 1440, 1512, 1568, 1584, 1600, 1620, 1656, 1728, 1764, 1800, 1836, 1872, 1936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Analogous to A005101 as A307958 is analogous to A000396.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

72 is in the sequence since its coreful divisors are 6, 12, 18, 24, 36, 72, whose sum is 168 > 2 * 72.

MATHEMATICA

f[p_, e_] := (p^(e+1)-1)/(p-1)-1; a[1]=1; a[n_] := Times @@ (f @@@ FactorInteger[n]); s={}; Do[If[a[n] > 2n, AppendTo[s, n]], {n, 1, 2000}]; s

PROG

(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947

s(n) = rad(n)*sigma(n/rad(n)); \\ A057723

isok(k) = s(k) > 2*k; \\ Michel Marcus, May 11 2019

CROSSREFS

Cf. A005101, A057723, A307958.

Sequence in context: A258695 A102562 A216426 * A307758 A272191 A072412

Adjacent sequences:  A308050 A308051 A308052 * A308054 A308055 A308056

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 10 2019

STATUS

approved

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Last modified May 15 17:50 EDT 2021. Contains 343920 sequences. (Running on oeis4.)