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%I #9 Feb 26 2023 03:26:43
%S 916352,3002751,13080447,22598271,26110592,28909952,45706112,49472127,
%T 52890624,53391231,56190591,58471552,63468927,65148543,67947903,
%U 69780608,84744063,89376128,93142143,94974848,143530623,143683712,145770111,155847807,165925503,177109375
%N Numbers k such that k and k+1 both have the same number of cubefree divisors and 3-full divisors.
%C Numbers k such that k and k+1 are both terms of A360906.
%H Amiram Eldar, <a href="/A360907/b360907.txt">Table of n, a(n) for n = 1..1000</a>
%e 48 is a term since A073184(916352) = A190867(916352) = 6 and A073184(916353) = A190867(916353) = 6.
%t 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]
%o (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)); }
%o lista(kmax) = {my(is1 = is(1), i2); for(k=2, kmax, is2 = is(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2); }
%Y Subsequence of A360906.
%Y Cf. A073184, A190867.
%K nonn
%O 1,1
%A _Amiram Eldar_, Feb 25 2023