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

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..7.

Example

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.

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]

Crossrefs

Cf. A356413, A356415.

Sequence in context: A266059 A356414 A020445 * A143252 A200565 A212609

Adjacent sequences: A356413 A356414 A356415 * A356417 A356418 A356419

Keyword

nonn,more

Author

Amiram Eldar, Aug 06 2022

Status

approved