A181597 (N\{4})-perfect numbers, i.e., numbers m for which sigma(m)-4 = 2m, if 4|m, otherwise sigma(m) = 2m.

6, 12, 88, 1888, 32128, 521728, 1848964, 8378368, 34359083008, 549753192448, 2251799645913088, 9223372026117357568, 2361183241263023915008, 865268370658615254581248

Offset

1,1

Comments

Or union of {6}, near-perfect numbers m (cf. A181595) for which d(m)=4, and all odd perfect numbers (if they exist). Note that (N\{2})-perfect numbers are numbers for which sigma(m)-2=2m, if m is even, and sigma(m)=2m, if m is odd. They are all even numbers of A045768 and all odd perfect numbers (if they exist).

Besides odd perfect numbers (if they exist), this sequence is formed by 6 followed by the multiples of 4 from A088832. - Max Alekseyev, Sep 02 2025

Links

Table of n, a(n) for n=1..14.

Example

88 is in the sequence since sigma(88) = 180 and 180 - 4 = 2*88.

Crossrefs

Cf. A000396, A005101, A005820, A088832, A118372, A153501, A181595, A181596.

Sequence in context: A054883 A005402 A128953 * A002898 A382772 A003613

Adjacent sequences: A181594 A181595 A181596 * A181598 A181599 A181600

Keyword

nonn,more

Author

Vladimir Shevelev, Nov 01 2010, Nov 03 2010

Extensions

Invalid term removed and a(8)-a(10) from Donovan Johnson, Sep 14 2013

a(11)-a(13) from Max Alekseyev, Sep 02 2025

a(14) from Max Alekseyev, Jan 27 2026

Status

approved