cp's OEIS Frontend

A386420 Odd numbers k that are closer to being perfect than previous terms and also satisfy the conditions that sigma(k) preserves the 3-adic valuation of k, and that sigma(k) == -k (mod 3).

%I A386420 #14 Jul 21 2025 13:12:52
%S A386420 7,15,105,495,1365,2205,9405,26145,31815,497835,654675,1984455,
%T A386420 7188885,9018009,9338595,9958905,13777785,13800465,14571585,47020995,
%U A386420 78867495,132884115,210124665,363860775
%N A386420 Odd numbers k that are closer to being perfect than previous terms and also satisfy the conditions that sigma(k) preserves the 3-adic valuation of k, and that sigma(k) == -k (mod 3).
%C A386420 Question: Is 2205 the only term also in A228058?
%C A386420 If it exists, a(25) > 1275068416.
%H A386420 <a href="/index/O#opnseqs">Index entries for sequences where (the least) odd perfect number must occur</a>
%o A386420 (PARI)
%o A386420 isA349752(n) = if(!(n%2), 0, my(s=sigma(n)); (0==(s+n)%3) && valuation(s, 3)==valuation(n, 3));
%o A386420 m=-1; n=0; k=0; while(m!=0, n++; if(!(n%(2^25)),print1("("n")")); if(isA349752(n), if((m<0) || abs((sigma(n)/n)-2)<m, m=abs((sigma(n)/n)-2); k++; write("b386420.txt", k, " ", n); print1(n, ", "))));
%Y A386420 Subsequence of A349752, thus also of A349749 and of A349751.
%Y A386420 Cf. A000203.
%Y A386420 Cf. also A171929, A228059, A386419, A386421, A386422.
%K A386420 nonn,more
%O A386420 1,1
%A A386420 _Antti Karttunen_, Jul 21 2025