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

1,1

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

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

Links

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

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

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

Sequence in context: A325798 A365830 A238524 * A378471 A237046 A370421

Adjacent sequences: A237284 A237285 A237286 * A237288 A237289 A237290

Keyword

nonn

Author

Jaroslav Krizek, Mar 02 2014

Extensions

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

Status

approved