A387405 a(n) is the least k that is a multiple of d=A240991(n), with abundancy ratio sigma(k)/k equal to (sigma(d)+1)/d), or -1 if no such k exists.

18, 54, 196, 1521, 486, 1372, 15376, 24025, 4374, 1032256, 67228, 39366, 476656, 257049, 744775, 27237961, 354294, 3341637, 3294172, 23088025, 870899121, 131096512, 3188646, 4990433449, 18837288001, 28697814, 43647148561, 458066416, 161414428, 131785698529, 8362054027, 274810802176, 564736653, 508339054441, 258280326

Offset: 1

Author

Antti Karttunen, Aug 30 2025

Keywords

• nonn
• new

Links

• Antti Karttunen, Table of n, a(n) for n = 1..67 (based on the b-file of A240991 as computed by Michel Marcus and Giovanni Resta)
• C. A. Holdener and J. A. Holdener, Characterizing Quasi-Friendly Divisors, Journal of Integer Sequences, Vol. 23 (2020), Article 20.8.4.

Crossrefs

Cf. A006530, A240991, A253560, A387406.

Programs

PARI

A387405(n) = { my(d=A240991(n), r=(sigma(d)+1)/d); forstep(k=d,oo,d,if(sigma(k)/k==r, return(k))); }

Formula

a(n) = A253560(A240991(n)) = A006530(A240991(n)) * A240991(n). - Conjectured, most likely true, especially if A240991 is a subsequence of A387406.