A356416 a(n) is the least start of exactly n consecutive numbers that have an equal sum of even and odd exponents in their prime factorization (A356413), or -1 if no such run of consecutive numbers exists.

1, 819, 1274, 19940, 204323, 149228720, 3144583275

Offset: 1

Author

Amiram Eldar, Aug 06 2022

Keywords

• nonn
• more

Comments

a(8) > 6.5*10^10, if it exists.

a(8) <= 604912797077420. - David A. Corneth, Aug 06 2022

Examples

			a(2) = 819 since 819 = 3^2 * 7 * 13 and 820 = 2^2 * 5 * 41 both have an equal sum of even and odd exponents (2) in their prime factorization, 818 and 821 have no even exponent, and 819 is the least number with this property.
		

Crossrefs

Cf. A356413, A356415.

Programs

Mathematica

f[p_, e_] := (-1)^e*e; q[1] = True; q[n_] := Plus @@ f @@@ FactorInteger[n] == 0; seq[len_, nmax_] := Module[{s = Table[0, {len}], v = {1}, n = 2, c = 0, m}, While[c <= len && n <= nmax, If[q[n], v = Join[v, {n}], m = Length[v]; v = {}; If[0 <= m <= len && s[[m]] == 0, c++; s[[m]] = n - m]]; n++]; s]; seq[4, 2*10^4]