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

1,1

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

Crossrefs

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

Sequence in context: A279420 A274051 A345069 * A130720 A046285 A048030

Adjacent sequences: A187709 A187710 A187711 * A187713 A187714 A187715

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 17 2011

Extensions

More terms from Amiram Eldar, Mar 22 2024

Status

approved