A374461 Numbers k such that k and k+1 are both nonsquarefree exponentially odd numbers (A374459).

135, 296, 343, 351, 375, 512, 999, 1160, 1375, 1431, 1592, 1624, 2079, 2295, 2375, 2456, 2727, 2943, 3104, 3159, 3429, 3591, 3624, 3752, 3992, 4023, 4184, 4616, 4832, 4887, 4913, 5048, 5144, 5319, 5480, 5535, 6183, 6344, 6375, 6655, 6858, 7047, 7263, 7479, 7624

Offset

1,1

Comments

The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 7, 59, 556, 5539, 55329, 553188, 5531116, 55311354, ... . Apparently, the asymptotic density of this sequence exists and equals 0.005531... .

Links

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

Example

135 is a term since both 135 = 3^3 * 5 and 136 = 2^3 * 17 are nonsquarefree exponentially odd numbers.

Mathematica

q[n_] := q[n] = Module[{e = FactorInteger[n][[;; , 2]]}, AllTrue[e, OddQ] && ! AllTrue[e, # == 1 &]]; Select[Range[10000], q[#] && q[# + 1] &]

Prog

(PARI) is1(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!(e[i] %2), return(0))); for(i = 1, #e, if(e[i] >1, return(1))); 0; }
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }

Crossrefs

Intersection of A068781 and A367695.

Subsequence of A268335 and A374459.

Sequence in context: A372567 A349176 A342189 * A176313 A372691 A335328

Adjacent sequences: A374458 A374459 A374460 * A374462 A374463 A374464

Keyword

nonn

Author

Amiram Eldar, Jul 09 2024

Status

approved