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.

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, 95, 97, 98, 99, 101, 102, 103, 105

Offset: 1

Author

Jaroslav Krizek, Mar 02 2014

Keywords

• nonn

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

First differs from A378471 at a(72). - Hartmut F. W. Hoft, Nov 27 2024

Examples

			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.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000203, A005153, A237046, A237289, A237290, A378471.

Programs

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).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

Extensions

More terms added by Hartmut F. W. Hoft, Nov 27 2024, in order to show the difference from A378471.