cp's OEIS Frontend

A122036 Odd abundant numbers (A005231) which are not in A136446, i.e., not sum of some of their proper divisors > 1.

%I A122036 #47 Jul 09 2025 04:26:12
%S A122036 351351
%N A122036 Odd abundant numbers (A005231) which are not in A136446, i.e., not sum of some of their proper divisors > 1.
%C A122036 It is conjectured that there are no odd weird numbers (A006037), i.e., that all odd abundant numbers (A005231) are pseudoperfect (A005835); this sequence lists those which are not equal to the sum of a subset of proper divisors > 1.
%C A122036 No second term in the range <= 53850001. - _R. J. Mathar_, Mar 21 2011
%C A122036 No other terms congruent to 21 (mod 30) below 10^9. - _M. F. Hasler_, Jul 16 2016
%C A122036 a(2) > 10^16. - _Wenjie Fang_, Jul 17 2017
%H A122036 <a href="/index/O#oneterm">Index entries for one-term sequences</a>
%e A122036 a(1) = 351351 = 3^3 * 7 * 11 * 13^2 is the sum of all its 47 proper divisors (including 1) except 7 and 11, but it is not possible to get the same sum without using the trivial divisor 1: The sum of all proper divisors *larger than 1* yields 351351 + 7 + 11 - 1 = 351351 + 17, and it is not possible to get 17 as sum of a subset of {3, 7, 9, 11, 13, 21, ...}. Thus, 351351 is not in A136446, and therefore in this sequence. - _M. F. Hasler_, Jul 16 2016, edited Mar 15 2021
%o A122036 (PARI) is_A122036(n)={n>351350 && !is_A005835(n,n=divisors(n)[2..-2]) && n && vecsum(n)>=n[1]*n[#n] && n[1]>2} \\ (Checking for abundant & odd after is_A005835() rather than before, to make it faster when operating on candidates known to satisfy these conditions.) Updated for current PARI syntax by _M. F. Hasler_, Jul 16 2016, further edits Jan 31 2020
%o A122036 forstep(n=1,10^7,2, is_A122036(n) && print1(n","))
%Y A122036 Cf. A005231, A005835, A006037, A136446.
%K A122036 nonn,bref,more,nice,hard
%O A122036 1,1
%A A122036 _N. J. A. Sloane_, Apr 11 2008, following correspondence from _R. K. Guy_, _M. F. Hasler_ and others
%E A122036 Comments and PARI code from _M. F. Hasler_, Apr 12 2008
%E A122036 Edited by _M. F. Hasler_, Jul 16 2016, Mar 15 2021