A349866 - OEIS

%I #10 Dec 03 2021 20:09:36

%S 4,45,6048,14421,26409026,29270772,30685402

%N Fixed points of A318996.

%C Integers m such that Sum_{d|m} (sigma(m) mod d) = m.

%H Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_1065.htm">Puzzle 1065. A larger integer than 45 such that ...</a>, The Prime Puzzles and Problems Connection.

%e The sum of divisors of 4 is 7 with divisors 1, 2, 4; And (7 mod 1) + (7 mod 2) + (7 mod 4) = 0 + 1 + 3 = 4.

%o (PARI) isok(m) = my(sn = sigma(m)); sumdiv(m, d, sn % d) == m;

%o (Python)

%o from itertools import count, islice

%o from sympy import divisor_sigma, divisors

%o def A349866gen(): # generator of terms

%o     return filter(lambda m: sum(divisor_sigma(m) % d for d in divisors(m,generator=True)) == m, count(1))

%o A349866_list = list(islice(A349866gen(),4)) # _Chai Wah Wu_, Dec 03 2021

%Y Cf. A000203, A318996.

%K nonn,more

%O 1,1

%A _Michel Marcus_, Dec 03 2021