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.

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

Author

Antti Karttunen, Jul 21 2025

Keywords

• nonn
• more

Comments

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.

Links

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

Crossrefs

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

Cf. also A119239, A171929, A228059.

Programs

PARI

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, ", ")));