A065235 - OEIS

%I #25 Nov 29 2024 08:10:09

%S 8925,32445,351351,442365,159427275,159587925,159677175,159784275,

%T 159837825,159855675,159944925,159962775,160016325,160105575,

%U 160266225,160284075,160391175,160444725,160480425,160533975,160551825,160766025,161015925,161033775,161069475

%N Odd numbers which can be written in precisely one way as sum of a subset of their proper divisors.

%C From _Antti Karttunen_, Nov 28 2024: (Start)

%C Characteristic function of this sequence is c(n) = A000035(n)*A378448(n).

%C The only non-multiples of 25 among the first 10000 terms are a(2)..(4): 32445 = 3^2 * 5 * 7 * 103, 351351 = 3^3 * 7 * 11 * 13^2 and 442365 = 3 * 5 * 7 * 11 * 383, while the other 9997 terms are all of the form 25 * some squarefree number. No terms of A228058 occur among the initial 10000 terms. Compare also to A348743.

%C (End)

%H Giovanni Resta, <a href="/A065235/b065235.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>

%F {k such that k is odd and A065205(k) = 1}. - _Antti Karttunen_, Nov 28 2024

%e See A064771 for an example when the number is even.

%Y Odd terms in A064771 (a unique subset of proper divisors sums to the number).

%Y Cf. A000035, A033630, A065205, A136446, A228058, A348743, A378448.

%K nonn

%O 1,1

%A _Jud McCranie_, Oct 23 2001

%E Definition clarified by _M. F. Hasler_, Apr 08 2008

%E More terms from _Giovanni Resta_, Oct 04 2019