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

1,1

Comments

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

Links

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

Example

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

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]

Prog

(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); }

Crossrefs

Subsequence of A360902.

A360905 is a subsequence.

Cf. A005361, A034444.

Sequence in context: A042105 A206046 A079240 * A275564 A275089 A235903

Adjacent sequences: A360901 A360902 A360903 * A360905 A360906 A360907

Keyword

nonn

Author

Amiram Eldar, Feb 25 2023

Status

approved