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A085844
Numbers equal to a permutation (or rearrangement) of the digits of the sum of their proper divisors. Rearrangements which cause leading zeros are excluded.
8
6, 28, 411, 496, 604, 1305, 3664, 4086, 4672, 4896, 5046, 7785, 8128, 8739, 9331, 14535, 16012, 18342, 18585, 19648, 20634, 21534, 21628, 22365, 25911, 27568, 28108, 29160, 29188, 31185, 32091, 32271, 34956, 35898, 35925, 36172, 37698, 40182, 54945, 56970
OFFSET
1,1
COMMENTS
Perfect numbers (A000396) are a subsequence. Perfect numbers are defined as numbers equal to the sum of their proper divisors. The numbers in this sequence are not perfect, but are "permutably perfect" since they are equal to a permutation of the sum of their proper divisors.
Note a(79)=195921 and a(80)=199251 and these are both permutations of each other. The same is true of a(90)=226944 and a(93)=244692.
EXAMPLE
604 is a term because the divisors of 604 are {1, 2, 4, 151, 302, 604} and 1 + 2 + 4 + 151 + 302 = 460.
16012 is included because it has the proper divisors 1, 2, 4, 4003, 8006. These divisors sum to 12016, which is a rearrangement of the digits of 16012.
PROG
(PARI) is_A085844(n)={vecsort(digits(n))==vecsort(digits(sigma(n)-n))} \\ M. F. Hasler, Feb 24 2014
(Python)
from sympy import divisors
def ok(n):
divs = divisors(n)[:-1]
return sorted(str(n)) == sorted(str(sum(divs)))
print(list(filter(ok, range(1, 57000)))) # Michael S. Branicky, Jun 28 2021
CROSSREFS
Cf. A000396.
Sequence in context: A332465 A335290 A173360 * A325638 A331752 A083387
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 05 2003; corrected Jul 07 2003
EXTENSIONS
Typo in example corrected by Alan Frank, Jan 20 2010
STATUS
approved