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 A236359 Pseudoperfect (or semiperfect) numbers in which a sum of contiguous proper divisors of n equals n. 2
 6, 18, 24, 28, 36, 42, 54, 66, 78, 102, 108, 114, 126, 132, 138, 162, 174, 186, 196, 198, 222, 234, 246, 258, 282, 288, 294, 306, 318, 324, 342, 354, 360, 366, 378, 402, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also includes perfect numbers. Are there numbers that contain multiple contiguous divisor sums? LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Matthew Schuster) Matthew Schuster, A236359.cpp; source file EXAMPLE 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. MATHEMATICA 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 *) Select[Range[800], MemberQ[Flatten[Table[Total/@Partition[Most[Divisors[ #]], n, 1], {n, DivisorSigma[0, #]-1}]], #]&] (* Harvey P. Dale, Apr 25 2015 *) PROG (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 (Python) from sympy import divisors A236359_list = [] for n in range(1, 10**3): ....d = divisors(n) ....d.pop() ....ld = len(d) ....if sum(d) >= n: ........s, j = d[0], 1 ........for i in range(ld-1): ............while s < n and j < ld: ................s += d[j] ................j += 1 ............if s == n: ................A236359_list.append(n) ................break ............j -= 1 ............s -= d[i]+d[j] # Chai Wah Wu, Sep 16 2014 CROSSREFS Subsequence of A005835. Sequence in context: A022418 A081318 A275168 * A011775 A015707 A236864 Adjacent sequences:  A236356 A236357 A236358 * A236360 A236361 A236362 KEYWORD nonn AUTHOR Matthew Schuster, Jan 23 2014 STATUS approved

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Last modified June 15 07:12 EDT 2021. Contains 345043 sequences. (Running on oeis4.)