A360907 Numbers k such that k and k+1 both have the same number of cubefree divisors and 3-full divisors.

916352, 3002751, 13080447, 22598271, 26110592, 28909952, 45706112, 49472127, 52890624, 53391231, 56190591, 58471552, 63468927, 65148543, 67947903, 69780608, 84744063, 89376128, 93142143, 94974848, 143530623, 143683712, 145770111, 155847807, 165925503, 177109375

Offset: 1

Author

Amiram Eldar, Feb 25 2023

Keywords

• nonn

Comments

Numbers k such that k and k+1 are both terms of A360906.

Examples

			48 is a term since A073184(916352) = A190867(916352) = 6 and A073184(916353) = A190867(916353) = 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A360906.

Cf. A073184, A190867.

Programs

Mathematica

q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Times @@ (Min[#, 3] & /@ (e + 1)) == Times @@ (Max[#, 1] & /@ (e - 1))]; 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, min(e[i] + 1, 3)) == prod(i = 1, #e, max(e[i] - 1, 1)); }
lista(kmax) = {my(is1 = is(1), i2); for(k=2, kmax, is2 = is(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2); }