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Numbers n that cannot be written as a sum of two or more distinct parts with the largest part dividing n.
2

%I #9 Sep 26 2023 15:35:04

%S 1,2,3,4,5,7,9,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,59,61,67,

%T 71,73,77,79,83,89,97,101,103,107,109,113,121,127,131,137,139,143,149,

%U 151,157,163,167,169,173,179,181,187,191,193,197,199,209,211,221

%N Numbers n that cannot be written as a sum of two or more distinct parts with the largest part dividing n.

%C After initial terms, first differs from A308168 in having 209.

%H Michael De Vlieger, <a href="/A327782/b327782.txt">Table of n, a(n) for n = 1..10000</a>

%H Francisco Javier de Vega, <a href="https://doi.org/10.3390/axioms12100905">Some Variants of Integer Multiplication</a>, Axioms (2023) Vol. 12, 905. See p. 8.

%t Select[Range[100],#==1||#-Divisors[#][[-2]]>Total[Range[Divisors[#][[-2]]-1]]&]

%Y Cf. A000009, A018818, A032742, A033630, A102627, A326836, A326837, A326841, A326850, A326851, A327783.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 25 2019