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
Examples
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.
Links
- Dumitru Damian, Table of n, a(n) for n = 1..235 (terms up to 10^9)
Programs
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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
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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
Extensions
a(22)-a(40) from Dumitru Damian, Feb 12 2024
Comments