login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A237287
Numbers that are not practical: positive integers n such that there exists at least one number k <= sigma(n) that is not a sum of distinct divisors of n.
7
3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94
OFFSET
1,1
COMMENTS
Complement of A005153 (practical numbers).
Numbers n such that A030057(n) < n.
First differs from A237046 at a(48).
First differs from A238524 at a(55). - Omar E. Pol, Mar 09 2014
LINKS
EXAMPLE
5 is in the sequence because there are 3 numbers <= sigma(5) = 6 that are not a sum of any subset of distinct divisors of 5: 2, 3 and 4.
PROG
(Python)
from itertools import count, islice
from sympy import factorint
def A237287_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
if m > 1:
l = (~m & m-1).bit_length()
if l>0:
P = (1<<l+1)-1
for p, e in factorint(m>>l).items():
if p > 1+P:
yield m
break
P *= (p**(e+1)-1)//(p-1)
else:
yield m
A237387_list = list(islice(A237287_gen(), 30)) # Chai Wah Wu, Jul 05 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 02 2014
STATUS
approved