cp's OEIS Frontend

A347882 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of 3. Here A003415 is the arithmetic derivative.

%I A347882 #16 Sep 19 2021 13:05:06
%S A347882 273,399,651,741,777,819,903,1197,1209,1281,1365,1407,1443,1533,1659,
%T A347882 1677,1767,1925,1953,1995,2035,2037,2109,2163,2223,2289,2331,2379,
%U A347882 2451,2457,2613,2667,2709,2847,2919,3003,3081,3171,3255,3297,3423,3441,3477,3591,3627,3685,3705,3783,3801,3819,3843,3885,3999,4017
%N A347882 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of 3. Here A003415 is the arithmetic derivative.
%C A347882 Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc. The square root of any hypothetical odd term appearing in A005820 should satisfy both conditions, and the term itself should appear in both A347383 and A347391.
%H A347882 Antti Karttunen, <a href="/A347882/b347882.txt">Table of n, a(n) for n = 1..10000</a>
%H A347882 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A347882 ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 4000, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 3] &] (* _Amiram Eldar_, Sep 18 2021 *)
%o A347882 (PARI)
%o A347882 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A347882 isA347882(n) = if(!(n%2),0,my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%3)));
%Y A347882 Cf. A000203, A003415, A005820, A097023, A342925, A342926, A347383, A347391.
%Y A347882 Subsequence of A347881. The intersection with A347887 gives A347888.
%Y A347882 Cf. also A342923.
%K A347882 nonn
%O A347882 1,1
%A A347882 _Antti Karttunen_, Sep 18 2021