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

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

Offset: 1

Author

Matthew Schuster, Jan 23 2014

Keywords

• nonn

Comments

Also includes perfect numbers.

Are there numbers that contain multiple contiguous divisor sums?

Examples

			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.
		

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

Crossrefs

Subsequence of A005835.

Programs

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 *)

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