

A122036


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


6




OFFSET

1,1


COMMENTS

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.
No second term in the range <= 53850001.  R. J. Mathar, Mar 21 2011
a(1) = 351351 = 3^3 * 7 * 11 * 13^2 is the sum of all its 47 proper divisors (including 1) except 7 and 11.  No other terms congruent to 21 (mod 30) below 10^9.  M. F. Hasler, Jul 16 2016
a(2) > 10^16.  Wenjie Fang, Jul 17 2017


LINKS

Table of n, a(n) for n=1..1.


PROG

(PARI) is_A122036(n)={n>351350 && !is_A005835(n, n=divisors(n)[2..2]) && n && vecsum(n)>=n[1]*n[#n] && n[1]>2} \\ Updated for current PARI syntax by M. F. Hasler, Jul 16 2016, further edits Jan 31 2020
forstep(n=1, 10^7, 2, is_A122036(n) && print1(n", "))


CROSSREFS

Cf. A005231, A005835, A006037, A136446.
Sequence in context: A213018 A274245 A274254 * A186822 A251246 A237098
Adjacent sequences: A122033 A122034 A122035 * A122037 A122038 A122039


KEYWORD

nonn,bref,more,nice


AUTHOR

N. J. A. Sloane, Apr 11 2008, following correspondence from R. K. Guy, M. F. Hasler and others.


EXTENSIONS

Comments and PARI code from M. F. Hasler, Apr 12 2008
Edited by M. F. Hasler, Jul 16 2016


STATUS

approved



