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.

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

Offset: 1

Author

Antti Karttunen, Sep 19 2021

Keywords

• nonn

Comments

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

Links

• Index entries for sequences related to sigma(n)

Crossrefs

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

Cf. A000203, A003415, A033880, A342926.

Programs

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 *)

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))(2*n)));