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A187712

Composite numbers k such that k = (product of divisors of k) mod (sum of divisors of k).

10, 20, 33, 40, 76, 136, 145, 207, 261, 385, 464, 528, 588, 897, 931, 1441, 1519, 1611, 1816, 1989, 2016, 2205, 2241, 2353, 3280, 3504, 3724, 3808, 4067, 4320, 4864, 5696, 6256, 7201, 7345, 8036, 10688, 10936, 11376, 13000, 16840, 17101, 18625, 19359, 19504, 19840

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OFFSET

1,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

FORMULA

A187711 INTERSECT A002808.

MATHEMATICA

Select[Range[20000], CompositeQ[#] && PowerMod[#, DivisorSigma[0, #]/2, DivisorSigma[1, #]] == # &] (* Amiram Eldar, Mar 22 2024 *)

PROG

(PARI) is1(n) = my(f = factor(n), s = sigma(f), d = numdiv(f)); if(d%2, Mod(sqrtint(n), s)^d, Mod(n, s)^(d/2)) == n;

is(n) = n > 1 && !isprime(n) && is1(n); \\ Amiram Eldar, Mar 22 2024