A279935 Numbers n such that n + sopf(n) + rad(n) = m and m - sopf(m) - rad(m) = n, where sopf(n) is the sum of the distinct primes dividing n and rad(n) is the squarefree kernel of n.

3, 4, 75, 112, 2057, 9178, 29818, 73813, 138992, 240469, 531002, 661489, 716856, 763648, 905474, 1033909, 1395554, 1572001, 1605519, 1643372, 1661030, 1692277, 1705724, 2312593, 2864773, 2911839, 2928193, 2977676, 3114366, 3744951, 4035647, 4122178, 4227036, 5716177

Offset

1,1

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..145

Example

Prime factors of 9178 are 2, 13, 353:
sopf(9178) = 2 + 13 + 353 = 368, rad(9178) = 2 * 13 * 353 = 9178 and 9178 + 368 + 9178 = 18724.
Prime factors of 18724 are 2, 2, 31, 151:
sopf(18724) = 2 + 31 + 151 = 184, rad(18724) = 2 * 31 * 151 = 9362 and 18724 - 184 - 9362 = 9178.

Maple

with(numtheory): P:=proc(q) local a, b, c, k, n; for n from 1 to q do
a:=ifactors(n)[2]; b:=mul(a[k][1], k=1..nops(a))+add(a[k][1], k=1..nops(a));
c:=n+b; a:=ifactors(c)[2]; b:=mul(a[k][1], k=1..nops(a))+add(a[k][1], k=1..nops(a));
d:=c-b; if d=n then print(n); fi; od; end: P(10^9);

Mathematica

f[n_] := Block[{pd = First@# & /@ FactorInteger@n}, Times @@ pd + Plus @@ pd]; fQ[n_] :=  n + f[n] - f[n + f[n]] == n; Select[ Range@ 1000000, fQ] (* Robert G. Wilson v, Dec 24 2016 *)

Crossrefs

Cf. A008472, A007947, A050780, A050781, A175760.

Sequence in context: A341851 A132414 A041171 * A111799 A135237 A316197

Adjacent sequences: A279932 A279933 A279934 * A279936 A279937 A279938

Keyword

nonn,easy

Author

Paolo P. Lava, Dec 23 2016

Status

approved