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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

%I #14 Jun 28 2021 08:56:41

%S 6,28,411,496,604,1305,3664,4086,4672,4896,5046,7785,8128,8739,9331,

%T 14535,16012,18342,18585,19648,20634,21534,21628,22365,25911,27568,

%U 28108,29160,29188,31185,32091,32271,34956,35898,35925,36172,37698,40182,54945,56970

%N Numbers equal to a permutation (or rearrangement) of the digits of the sum of their proper divisors. Rearrangements which cause leading zeros are excluded.

%C 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.

%C 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.

%H V. Raman, <a href="/A085844/b085844.txt">Table of n, a(n) for n = 1..10000</a>

%e 604 is a term because the divisors of 604 are {1, 2, 4, 151, 302, 604} and 1 + 2 + 4 + 151 + 302 = 460.

%e 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.

%o (PARI) is_A085844(n)={vecsort(digits(n))==vecsort(digits(sigma(n)-n))} \\ _M. F. Hasler_, Feb 24 2014

%o (Python)

%o from sympy import divisors

%o def ok(n):

%o divs = divisors(n)[:-1]

%o return sorted(str(n)) == sorted(str(sum(divs)))

%o print(list(filter(ok, range(1, 57000)))) # _Michael S. Branicky_, Jun 28 2021

%Y Cf. A000396.

%K base,nonn

%O 1,1

%A Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 05 2003; corrected Jul 07 2003

%E Typo in example corrected by _Alan Frank_, Jan 20 2010

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)