A203616 Numbers k such that the reversal of sigma*(k) equals the sum of the reversals of the anti-divisors of k, where sigma*(k) is the sum of the anti-divisors of k.

1, 2, 3, 4, 5, 6, 8, 9, 20, 63, 96, 97, 317, 596, 1473, 3934, 26777, 27684, 50867, 51767, 62417, 322001, 393216, 1308775, 1420260, 1851474, 2651867, 2659067, 3040656, 3227267, 3289277, 3376007, 4626917, 4639067, 5378507, 6054521, 6227027, 6239839, 6439067, 6581929

Offset

1,2

Comments

A066466 is a subsequence of this sequence.

Links

Dumitru Damian, Table of n, a(n) for n = 1..235 (terms up to 10^9)

Example

n=317. Anti-divisors: 2, 3, 5, 127, 211.
Sum of the reversals of the anti-divisors: 2+3+5+721+112=843.
Sigma*(317)=348 and its reversal is 843.
n=1473. Anti-divisors: 2, 5, 6, 7, 19, 31, 95, 155, 421, 589, 982.
Sum of the reversals of the anti-divisors:
2+5+6+7+91+13+59+551+124+985+289=2132.
Sigma*(1473)=2312 and its reversal is 2132.

Maple

isA203616:=proc(j) local a, b, c;   a:=0; b:=0;
   for c from 2 to j-1 do
     if abs((j mod c)-c/2)<1 then a:=a+A004086(c); b:=b+c; fi;
   od;
evalb(A004086(b)=a) end: # simplified by M. F. Hasler, Jan 29 2012
for n to 10^7 do if isA203616(n) then lprint(n) fi od: # simplified by M. F. Hasler, Jan 29 2012

Prog

(Python)
from itertools import count, islice
from sympy.ntheory.factor_ import antidivisors
def a203616():
    isa = lambda n: str(sum((a:=antidivisors(n))))[::-1]==str(sum(map(int, (str(_)[::-1] for _ in a))))
    yield from (n for n in count(1) if isa(n))
a203616_list = [*islice(a203616(), 20)] # Dumitru Damian, Feb 12 2024

Crossrefs

Cf. A004086, A066272, A066466, A069942, A195144, A203615.

Sequence in context: A002242 A317676 A039125 * A274049 A038101 A073956

Adjacent sequences: A203613 A203614 A203615 * A203617 A203618 A203619

Keyword

nonn,base

Author

Paolo P. Lava, Jan 20 2012

Extensions

a(22)-a(40) from Dumitru Damian, Feb 12 2024

Status

approved