A356414 Number k such that k and k+1 both have an equal sum of even and odd exponents in their prime factorization (A356413).

819, 1035, 1196, 1274, 1275, 1449, 1665, 1924, 1925, 1988, 2324, 2331, 2540, 3068, 3195, 3324, 3339, 3549, 3555, 3626, 3717, 4164, 4220, 4235, 4556, 4598, 4635, 4675, 4796, 5084, 5525, 5634, 5660, 6003, 6027, 6068, 6164, 6363, 6740, 6867, 6908, 7028, 7227, 7275

Offset

1,1

Comments

Numbers k such that A350386(k) = A350387(k) and A350386(k+1) = A350387(k+1).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

819 is a term since A350386(819) = A350387(819) = 2 and A350386(820) = A350387(820) = 2.

Mathematica

f[p_, e_] := (-1)^e*e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; Select[Range[10^4], q[#] && q[# + 1] &]

Prog

(PARI) is(n) = {my(f = factor(n)); sum(i = 1, #f~, (-1)^f[i, 2]*f[i, 2]) == 0};
is1 = is(1); for(k = 2, 10^4, is2 = is(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2);

Crossrefs

Cf. A350386, A350387, A356413.

Sequence in context: A105989 A332181 A266059 * A020445 A356416 A143252

Adjacent sequences: A356411 A356412 A356413 * A356415 A356416 A356417

Keyword

nonn

Author

Amiram Eldar, Aug 06 2022

Status

approved