A065235 Odd numbers which can be written in precisely one way as sum of a subset of their proper divisors.

8925, 32445, 351351, 442365, 159427275, 159587925, 159677175, 159784275, 159837825, 159855675, 159944925, 159962775, 160016325, 160105575, 160266225, 160284075, 160391175, 160444725, 160480425, 160533975, 160551825, 160766025, 161015925, 161033775, 161069475

Offset: 1

Author

Jud McCranie, Oct 23 2001

Keywords

• nonn

Comments

From Antti Karttunen, Nov 28 2024: (Start)

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

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.

(End)

Examples

			See A064771 for an example when the number is even.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Index entries for sequences where any odd perfect numbers must occur

Crossrefs

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

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

Formula

{k such that k is odd and A065205(k) = 1}. - Antti Karttunen, Nov 28 2024

Extensions

Definition clarified by M. F. Hasler, Apr 08 2008

More terms from Giovanni Resta, Oct 04 2019