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A236359 Pseudoperfect (or semiperfect) numbers in which a sum of contiguous proper divisors of n equals n. 1
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

Matthew Schuster and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from 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]; only the contiguous divisor set of 4+6+11+12+22+33+44=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 September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)