A360904 Numbers k such that k and k+1 both have the same number of squarefree divisors and powerful divisors.

48, 2511, 5328, 6723, 7856, 10287, 15471, 15632, 16640, 18063, 20816, 28592, 33124, 36368, 38799, 39600, 40400, 40816, 54512, 57121, 60624, 67472, 75248, 79375, 83024, 88047, 93231, 101168, 119375, 126927, 134703, 137456, 146688, 147824, 148224, 154448, 160624

Offset: 1

Author

Amiram Eldar, Feb 25 2023

Keywords

• nonn

Comments

Numbers k such that k and k+1 are both terms of A360902.

Examples

			48 is a term since A034444(48) = A005361(48) = 4 and A034444(49) = A005361(49) = 2.
		

Links

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

Crossrefs

Subsequence of A360902.

A360905 is a subsequence.

Cf. A005361, A034444.

Programs

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Times @@ e == 2^Length[e]]; q[1] = True; seq[kmax_] := Module[{s = {}, k = 1, q1 = q[1], q2}, Do[q2 = q[k]; If[q1 && q2, AppendTo[s, k-1]]; q1 = q2, {k, 2, kmax}]; s]; seq[2*10^5]

PARI

is(k) = {my(e = factor(k)[,2]); prod(i = 1, #e, e[i]) == 2^#e; }
lista(kmax) = {my(is1 = is(1), i2); for(k=2, kmax, is2 = is(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2); }