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.

1, 3, 9, 21, 63, 135, 855, 1485, 25245, 34155, 43785, 46035, 1665825, 1805475, 22982505, 125011845, 127371195, 657814575

Offset: 1

Author

Antti Karttunen, Jul 21 2025

Keywords

• nonn
• more

Comments

Questions: Are there only multiples of 5 after the five initial terms? Are there any common terms with A228058?

Links

• Index entries for sequences where (the least) odd perfect number must occur
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Subsequence of A349174.

Cf. A000203, A000396, A003961.

Cf. also A171929, A228059, A386419, A386420, A386422 for similar sequences.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
is_A349174(n) = if(!(n%2), 0, my(u=A003961(n)); gcd(u, sigma(n))==gcd(u, n));
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)