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!)
A258270 Consider the unitary aliquot parts, in ascending order, of a composite number. Take their sum and repeat the process deleting the minimum number and adding the previous sum. The sequence lists the numbers that after some iterations reach a sum equal to the reverse of themselves. 1
6, 75, 133, 1005, 1603, 4258, 5299, 84292, 89944, 170568, 192901, 303003, 695364, 1633303 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Eric Weisstein's World of Mathematics, Unitary Divisor

Eric Weisstein's World of Mathematics, Unitary Divisor Function

Eric Weisstein's World of Mathematics, Unitary Perfect Number

Wikipedia, Unitary divisor

EXAMPLE

Divisors of 6 are 1, 2, 3, 6. Unitary aliquot parts are 1, 2, 3.

We have: 1 + 2 + 3 = 6 that is equal to its reverse;

Divisors of 75 are 1, 3, 5, 15, 25, 75.

Unitary aliquot parts are 1, 3, 25. We have:

1 + 3 + 25 = 29;

3 + 25 + 29 = 57 that is the reverse of 75;

Divisors of 84292 are 1, 2, 4, 13, 26, 52, 1621, 3242, 6484, 21073, 42146, 84292. Unitary aliquot parts are 1, 4, 13, 52, 1621, 6484, 21073. We have:

1 + 4 + 13 + 52 + 1621 + 6484 + 21073 = 29248 that is the reverse of 84292;

MAPLE

with(numtheory): R:=proc(w) local x, y; x:=w; y:=0; while x>0 do

y:=10*y+(x mod 10); x:=trunc(x/10); od: y; end:

P:=proc(q, h) local a, b, c, k, n, t, v; v:=array(1..h);

for n from 1 to q do if not isprime(n) then a:=sort([op(divisors(n))]);

b:=[]; c:=ilog10(n)+1; for k from 1 to nops(a)-1 do if gcd(a[k], n/a[k])=1

then b:=[op(b), a[k]]; fi; od; if nops(b)>1 then

for k from 1 to nops(b) do v[k]:=b[k]; od; t:=nops(b)+1; v[t]:=add(v[k], k=1..nops(b)); if R(v[t])=n then print(n); else

while ilog10(v[t])+1<=c do t:=t+1; v[t]:=add(v[k], k=t-nops(b)..t-1);

if R(v[t])=n then print(n); break; fi; od; fi; fi; fi; od;

end: P(10^9, 1000);

CROSSREFS

Cf. A246544, A247012, A258142.

Sequence in context: A269334 A069852 A266574 * A281797 A049235 A129031

Adjacent sequences:  A258267 A258268 A258269 * A258271 A258272 A258273

KEYWORD

nonn,more,base

AUTHOR

Paolo P. Lava, May 25 2015

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 May 24 19:38 EDT 2022. Contains 354043 sequences. (Running on oeis4.)