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A338504
Number of integers less than n with the same sum of proper divisors as n.
0
0, 0, 1, 0, 2, 0, 3, 0, 0, 0, 4, 0, 5, 0, 0, 0, 6, 0, 7, 0, 0, 0, 8, 0, 1, 1, 0, 0, 9, 0, 10, 0, 1, 0, 1, 0, 11, 1, 0, 0, 12, 0, 13, 0, 0, 0, 14, 0, 1, 0, 1, 0, 15, 0, 1, 0, 0, 0, 16, 0, 17, 0, 0, 0, 0, 0, 18, 0, 0, 0, 19, 0, 20, 1, 0, 1, 1, 0, 21, 0, 2, 0, 22, 0, 1, 1, 1, 0, 23, 0, 2
OFFSET
1,5
FORMULA
a(n) = |{j < n : sigma(j) - j = sigma(n) - n}|.
EXAMPLE
a(5) = 2 because A001065(5) = 1 and also A001065(2) = A001065(3) = 1.
MATHEMATICA
Table[Length[Select[Range[n - 1], DivisorSigma[1, #] - # == DivisorSigma[1, n] - n &]], {n, 91}]
PROG
(PARI) a(n)={my(t=sigma(n)-n); sum(k=1, n-1, sigma(k)-k==t)} \\ Andrew Howroyd, Oct 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 31 2020
STATUS
approved