A171929 -id:A171929 - 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.

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

Offset: 1

Antti Karttunen, Jul 21 2025

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

Subsequence of A349174.
Cf. A000203, A000396, A003961.
Cf. also A171929, A228059, A386419, A386420, A386422 for similar sequences.

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)

A386423 Odd numbers k such that k/(1+A347381(k)) obtains record values, where A347381 gives the distance from n to the nearest common ancestor of n and sigma(n) in the Doudna-tree.

Original entry on oeis.org

1, 3, 5, 9, 13, 15, 35, 63, 77, 81, 99, 105, 135, 175, 189, 455, 765, 775, 819, 945, 2125, 6375, 9261, 21275, 43011, 43125, 43475, 44469, 45441, 45617, 45619, 46189, 46305, 155363, 161257, 203203, 318835, 401625, 1016015, 1128799, 1773827, 3048045, 3255075, 3386397, 4044555

Offset: 1

Antti Karttunen, Jul 21 2025

Odd terms of A347391 probably form a subsequence, especially if there are no odd perfect numbers or other odd terms larger than one in A336702.

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Cf. A000203, A005940, A336702, A347381, A347391.

Cf. also A119239, A171929, A228059.

m=-1; n=-1; k=0; while(m!=0, n+=2; if(!((n-1)%(2^25)),print1("("n")")); my(r=n/(1+A347381(n))); if(r>m, m=r; k++; write("b386423.txt", k, " ", n); print1(n, ", ")));

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.

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