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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..91.

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

Cf. A001065, A047983, A263025.

Sequence in context: A104117 A114511 A085199 * A085200 A080024 A348223

Adjacent sequences:  A338501 A338502 A338503 * A338505 A338506 A338507

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 31 2020

STATUS

approved

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)