A190104 Let sopfr(k) = A001414(k) denote the sum of the prime factors of k with multiplicity. This sequence lists the numbers k such that if sopfr(k) = m and sopfr(m) = r, then k == r (mod m) with 0 < r < m.

24, 57, 135, 168, 200, 222, 512, 575, 585, 713, 760, 781, 825, 854, 1161, 1360, 1475, 1484, 1485, 1504, 1780, 1872, 1960, 2415, 2444, 2535, 2784, 3087, 3096, 3168, 3216, 3250, 3360, 3404, 3531, 3596, 3844, 3850, 4235, 4240, 4410, 4437, 4512, 4514, 4810

Offset

1,1

Comments

Trivial solutions with sopfr(k) = k and thus r = 0 are excluded.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For k = 200, sopfr(200) = 2+2+2+5+5 = 16; 200 == 8 (mod 16); and sopfr(16) = 2+2+2+2 = 8 = r.

Maple

sopfr:= proc(n) local t;
  add(t[1]*t[2], t = ifactors(n)[2])
end proc:
filter:= proc(k) local m, r;
    m:= sopfr(k);
    r:= sopfr(m);
    r > 0 and r < m and k - r mod m = 0
end proc:
select(filter, [$1..10000]); # Robert Israel, Dec 19 2024

Crossrefs

Cf. A001414.

Sequence in context: A211461 A208086 A232937 * A255968 A211325 A290303

Adjacent sequences: A190101 A190102 A190103 * A190105 A190106 A190107

Keyword

nonn

Author

J. M. Bergot, May 04 2011

Extensions

Extended by Ray Chandler, May 11 2011

Status

approved