login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A352337 Numbers m such that A_m(j) = 1 for some value of j, where A_m(k+1) = 2*A_m(k) - sigma(A_m(k)), sigma(m) = sum of the divisors of m, and A_m(1) = m. 0
1, 2, 3, 4, 5, 8, 9, 10, 11, 14, 16, 17, 21, 22, 23, 26, 27, 32, 34, 35, 38, 39, 44, 55, 57, 58, 59, 63, 64, 68, 74, 75, 77, 82, 83, 92, 93, 94, 110, 116, 119, 122, 125, 128, 129, 130, 131, 134, 136, 137, 142, 145, 152, 161, 164, 170, 171, 184, 185, 189, 194 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
If m is deficient, then 2m > sigma(m) (see A005100) and the deficiency of m is defined as 2m - sigma(m) (see A033879). Now you can check if the deficiency is also deficient and generalize this with A_m(k+1) = 2*A_m(k) - sigma(A_m(k)) and A_m(1) = m. If A_m(j) = 1 for some value of j, then m is in this sequence.
This sequence is a subsequence of A005100 (deficient numbers), because if m is abundant or perfect (see A005101 and A000396) then A_m(2) = 2*m - sigma(m) <= 0 instantly.
Since it is conjectured that 2m - sigma(m) = 1 only for m which are powers of two (see comments at A237588) all numbers in this sequence must have one k for which A_m(k) is a power of two.
Because of 2*2^k - sigma(2^k) = 1 all powers of two are in this sequence and with that this sequence has infinitely many terms. Further all Fermat primes (see A019434) are also in this sequence.
LINKS
EXAMPLE
11 is in this sequence because A_11(1) = 11, A_11(2) = 2*11-(1+11) = 10, A_11(3) = 2*10-(1+2+5+10) = 2, A_11(4) = 2*2-(2+1) = 1.
PROG
(PARI) f(n) = 2*n - sigma(n);
isok(m) = while (1, m = f(m); if (m==1, return(1)); if (m<=0, return(0)); ); \\ Michel Marcus, Mar 13 2022
CROSSREFS
Subsequence of A005100.
Sequence in context: A169606 A140769 A364380 * A032877 A032844 A023775
KEYWORD
nonn
AUTHOR
Simon Wundling, Mar 13 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)