cp's OEIS Frontend

A340229 Numbers m such that numbers m, m + 1, m + 2, m + 3 and m + 4 have k, 2k, 4k, 8k and 16k divisors respectively.

%I A340229 #12 Sep 08 2022 08:46:26
%S A340229 1124581,2101621,2135701,3829381,5801701,6097381,6453541,6535861,
%T A340229 6609781,6799621,6972661,7055317,7527061,8281381,8485502,8524981,
%U A340229 8883326,9412981,9895141,11455141,11901781,12043621,12929941,13749061,14747701,15150901,15504661,15533941
%N A340229 Numbers m such that numbers m, m + 1, m + 2, m + 3 and m + 4 have k, 2k, 4k, 8k and 16k divisors respectively.
%C A340229 Numbers m such that tau(m) = tau(m + 1)/2 = tau(m + 2)/4 = tau(m + 3)/8 = tau(m + 4)/16, where tau(k) = the number of divisors of k (A000005).
%C A340229 Quintuples of [tau(a(n)), tau(a(n) + 1), tau(a(n) + 2), tau(a(n) + 3), tau(a(n) + 4)] = [tau(a(n)), 2*tau(a(n)), 4*tau(a(n)), 8*tau(a(n)), 16*tau(a(n))]: [2, 4, 8, 16, 32], [2, 4, 8, 16, 32], [2, 4, 8, 16, 32], [2, 4, 8, 16, 32], [2, 4, 8, 16, 32], [2, 4, 8, 16, 32], ...
%C A340229 Corresponding values of numbers k: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 4, ...
%C A340229 Prime terms are in A100365; number 8485502 is the smallest composite term.
%C A340229 Subsequence of A063446, A100363 and A100364.
%e A340229 tau(1124581) = 2, tau(1124582) = 4, tau(1124583) = 8, tau(1124584) = 16, tau (1124585) = 32.
%o A340229 (Magma) [m: m in [1..10^7] | #Divisors(m) eq #Divisors(m + 1) / 2 and #Divisors(m) eq #Divisors(m + 2) / 4 and #Divisors(m) eq #Divisors(m + 3) / 8 and #Divisors(m) eq #Divisors(m + 4) / 16]
%o A340229 (PARI) isok(m) = vector(4, k, numdiv(m+k))/numdiv(m) == [2,4,8,16]; \\ _Michel Marcus_, Jan 02 2021
%Y A340229 Cf. A000005, A063446, A100363, A100364, A100365, A340230.
%K A340229 nonn
%O A340229 1,1
%A A340229 _Jaroslav Krizek_, Jan 01 2021