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

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 17 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A002808, A007955, A187680, A187711.

Programs

Mathematica

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

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

Formula

A187711 INTERSECT A002808.

Extensions

More terms from Amiram Eldar, Mar 22 2024