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A236359 Pseudoperfect (or semiperfect) numbers in which a sum of contiguous proper divisors of n equals n.

%I A236359 #34 May 22 2025 10:21:36
%S A236359 6,18,24,28,36,42,54,66,78,102,108,114,126,132,138,162,174,186,196,
%T A236359 198,222,234,246,258,282,288,294,306,318,324,342,354,360,366,378,402,
%U A236359 414,426,432,438,462,474,486,496,498,504,522,534,540,546,558,582,594,600,606,618,642,654,666,678,684,690,696,702,714,726
%N A236359 Pseudoperfect (or semiperfect) numbers in which a sum of contiguous proper divisors of n equals n.
%C A236359 Also includes perfect numbers.
%C A236359 Are there numbers that contain multiple contiguous divisor sums?
%H A236359 Charles R Greathouse IV, <a href="/A236359/b236359.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Matthew Schuster)
%H A236359 Matthew Schuster, <a href="/A236359/a236359.cpp.txt">A236359.cpp; source file</a>
%e A236359 The proper divisors of 132 are [1,2,3,4,6,11,12,22,33,44,66]; the contiguous divisor set 4,6,11,12,22,33,44 sums to 132.
%t A236359 aQ[n_] := Catch@Block[{d = Most@Divisors@n, s, i=1}, s = Accumulate@d; While[s != {}, If[MemberQ[s, n], Throw@True, s = Rest[s - d[[i++]]]]]; False]; Select[ Range@ 726, aQ] (* _Giovanni Resta_, Jan 23 2014 *)
%t A236359 Select[Range[800],MemberQ[Flatten[Table[Total/@Partition[Most[Divisors[ #]],n,1],{n,DivisorSigma[0,#]-1}]],#]&] (* _Harvey P. Dale_, Apr 25 2015 *)
%o A236359 (PARI) is(n)=my(d=divisors(n),i=1,j=1,s=1); while(i<#d, s+=d[i++]; while(s>n, s-=d[j]; j++); if(s==n, return(i<#d))); 0 \\ _Charles R Greathouse IV_, Jan 23 2014
%o A236359 (Python)
%o A236359 from sympy import divisors
%o A236359 A236359_list = []
%o A236359 for n in range(1,10**3):
%o A236359     d = divisors(n)
%o A236359     d.pop()
%o A236359     ld = len(d)
%o A236359     if sum(d) >= n:
%o A236359         s, j = d[0], 1
%o A236359         for i in range(ld-1):
%o A236359             while s < n and j < ld:
%o A236359                 s += d[j]
%o A236359                 j += 1
%o A236359             if s == n:
%o A236359                 A236359_list.append(n)
%o A236359                 break
%o A236359             j -= 1
%o A236359             s -= d[i]+d[j] # _Chai Wah Wu_, Sep 16 2014
%Y A236359 Subsequence of A005835.
%K A236359 nonn
%O A236359 1,1
%A A236359 _Matthew Schuster_, Jan 23 2014