cp's OEIS Frontend

A386426 Odd nondeficient numbers k such that sigma(k) has the same powerful part as k, where sigma is the sum of divisors function.

%I A386426 #34 Aug 21 2025 14:37:16
%S A386426 81022725,891360225,992106225,1863765225,2349967725,3322372725,
%T A386426 7211992725,8670600225,9156802725,11101612725,13208490225,15477435225,
%U A386426 15963637725,18394650225,18880852725,21311865225,21960135225,22446337725,22932540225,25687687725,25849755225,28280767725,28604902725,30711780225,31035915225
%N A386426 Odd nondeficient numbers k such that sigma(k) has the same powerful part as k, where sigma is the sum of divisors function.
%C A386426 Sequence by definition contains also any such hypothetical odd terms of A007691 that are mentioned in the comments of A386425. However, if no such terms exist, then this is a subsequence of A386427.
%C A386426 This sequence contains also the intersection of A001694 and A386425, even though it is probably an empty set. See comments in A386428.
%C A386426 The first three terms not divisible by 25 are: a(191) = 283806508293, a(247) = 371184932349, a(328) = 502252568433.
%H A386426 Giovanni Resta, <a href="/A386426/b386426.txt">Table of n, a(n) for n = 1..400</a>
%H A386426 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%H A386426 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>.
%F A386426 {k | k is odd, A000203(k) >= 2*k and A003557(A000203(k)) = A003557(k)}.
%o A386426 (PARI)
%o A386426 A057521(n)=my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1))
%o A386426 isA386426(n) = if(!(n%2), 0, my(s=sigma(n)); ((s>=(2*n)) && (A057521(s)==A057521(n))));
%Y A386426 Intersection of A023196 and A386425.
%Y A386426 Conjectured to be a subsequence of A386427.
%Y A386426 Cf. A000203, A001694, A003557, A007691, A057521, A386428.
%Y A386426 Cf. also A005231.
%K A386426 nonn,new
%O A386426 1,1
%A A386426 _Antti Karttunen_, Aug 17 2025
%E A386426 a(8)-a(25) from _Giovanni Resta_, Aug 18 2025