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A355712 Starts of runs of 4 consecutive numbers with the same number of 5-smooth divisors.

%I A355712 #10 Jul 19 2022 08:03:05
%S A355712 28374,133623,136374,187623,190374,298374,349623,352374,457623,460374,
%T A355712 511623,619623,622374,673623,676374,781623,838374,943623,946374,
%U A355712 997623,1000374,1108374,1159623,1162374,1267623,1270374,1321623,1429623,1432374,1483623,1486374,1591623
%N A355712 Starts of runs of 4 consecutive numbers with the same number of 5-smooth divisors.
%C A355712 Numbers k such that A355583(k) = A355583(k+1) = A355583(k+2) = A355583(k+3).
%C A355712 Are there runs of 5 consecutive numbers with the same number of 5-smooth divisors? There are no such runs below 10^10.
%H A355712 Amiram Eldar, <a href="/A355712/b355712.txt">Table of n, a(n) for n = 1..10000</a>
%e A355712 28374 is a term since A355583(28374) = A355583(28375) = A355583(28376) = A355583(28377) = 4.
%t A355712 f[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); s = {}; m = 4; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^6}]; s
%o A355712 (PARI) s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
%o A355712 s1 = s(1); s2 = s(2); s3 = s(3); for(k = 4, 1.6e6, s4 = s(k); if(s1 == s2 && s2 == s3 && s3 == s4, print1(k-3,", ")); s1 = s2; s2 = s3; s3 = s4);
%Y A355712 Cf. A355583.
%Y A355712 Subsequence of A355710 and A355711.
%Y A355712 Similar sequences: A006601, A332314, A332388.
%K A355712 nonn
%O A355712 1,1
%A A355712 _Amiram Eldar_, Jul 15 2022