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A347889 Numbers k such that sigma(k) > 2*k and A003415(sigma(k)) < k, where A003415 is the arithmetic derivative, and sigma is the sum of divisors function. 2
18, 36, 100, 144, 324, 400, 576, 784, 900, 1296, 1458, 1600, 1936, 2304, 2500, 2704, 2916, 3136, 3600, 4624, 5184, 5202, 5776, 6400, 7744, 8464, 9216, 9604, 10000, 10404, 10816, 11664, 12100, 13122, 13456, 14400, 15376, 17424, 18496, 19044, 23104, 25600, 26244, 28900, 30258, 30276, 30976, 32400, 33856, 36864, 38416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k such that A033880(k) is positive but A342926(k) is negative.

LINKS

Table of n, a(n) for n=1..51.

Index entries for sequences related to sigma(n)

MATHEMATICA

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 40000], DivisorSigma[1, #] > 2*# && ad[DivisorSigma[1, #]] < # &] (* Amiram Eldar, Sep 19 2021 *)

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

isA347889(n) = ((A003415(sigma(n))<n)&&(sigma(n)>(2*n)));

CROSSREFS

Intersection of A005101 and A343216. Subsequence A347890 gives the odd terms.

Cf. A000203, A003415, A033880, A342926.

Sequence in context: A252424 A327774 A335784 * A115550 A061713 A198802

Adjacent sequences:  A347886 A347887 A347888 * A347890 A347891 A347892

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 19 2021

STATUS

approved

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Last modified July 4 22:49 EDT 2022. Contains 355086 sequences. (Running on oeis4.)