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

1,1

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