cp's OEIS Frontend

A386421 Odd numbers k that are closer to being perfect than previous terms and also satisfy the condition that gcd(k, A003961(k)) is equal to gcd(sigma(k), A003961(k)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

%I A386421 #8 Jul 21 2025 13:13:01
%S A386421 1,3,9,21,63,135,855,1485,25245,34155,43785,46035,1665825,1805475,
%T A386421 22982505,125011845,127371195,657814575
%N A386421 Odd numbers k that are closer to being perfect than previous terms and also satisfy the condition that gcd(k, A003961(k)) is equal to gcd(sigma(k), A003961(k)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.
%C A386421 Questions: Are there only multiples of 5 after the five initial terms? Are there any common terms with A228058?
%H A386421 <a href="/index/O#opnseqs">Index entries for sequences where (the least) odd perfect number must occur</a>
%H A386421 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A386421 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A386421 (PARI)
%o A386421 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A386421 is_A349174(n) = if(!(n%2), 0, my(u=A003961(n)); gcd(u, sigma(n))==gcd(u, n));
%o A386421 m=-1; n=-1; k=0; while(m!=0, n+=2; if(!((n-1)%(2^25)),print1("("n")")); if(is_A349174(n), if((m<0) || abs((sigma(n)/n)-2)<m, m=abs((sigma(n)/n)-2); k++; write("b386421.txt", k, " ", n); print1(n, ", "))));
%Y A386421 Subsequence of A349174.
%Y A386421 Cf. A000203, A000396, A003961.
%Y A386421 Cf. also A171929, A228059, A386419, A386420, A386422 for similar sequences.
%K A386421 nonn,more
%O A386421 1,2
%A A386421 _Antti Karttunen_, Jul 21 2025