cp's OEIS Frontend

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.

%I A347889 #12 Sep 19 2021 22:02:46
%S A347889 18,36,100,144,324,400,576,784,900,1296,1458,1600,1936,2304,2500,2704,
%T A347889 2916,3136,3600,4624,5184,5202,5776,6400,7744,8464,9216,9604,10000,
%U A347889 10404,10816,11664,12100,13122,13456,14400,15376,17424,18496,19044,23104,25600,26244,28900,30258,30276,30976,32400,33856,36864,38416
%N 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.
%C A347889 Numbers k such that A033880(k) is positive but A342926(k) is negative.
%H A347889 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A347889 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 *)
%o A347889 (PARI)
%o A347889 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347889 isA347889(n) = ((A003415(sigma(n))<n)&&(sigma(n)>(2*n)));
%Y A347889 Intersection of A005101 and A343216. Subsequence A347890 gives the odd terms.
%Y A347889 Cf. A000203, A003415, A033880, A342926.
%K A347889 nonn
%O A347889 1,1
%A A347889 _Antti Karttunen_, Sep 19 2021