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A355710 Numbers k such that k and k+1 have the same number of 5-smooth divisors.

%I A355710 #11 Jul 19 2022 08:03:00
%S A355710 2,21,33,34,38,57,85,86,93,94,104,116,122,141,145,146,154,158,171,177,
%T A355710 182,189,201,205,213,214,218,237,265,266,273,296,302,321,326,332,334,
%U A355710 338,344,357,362,381,385,387,393,394,398,417,445,446,453,454,475,476,482
%N A355710 Numbers k such that k and k+1 have the same number of 5-smooth divisors.
%C A355710 Numbers k such that A355583(k) = A355583(k+1).
%H A355710 Amiram Eldar, <a href="/A355710/b355710.txt">Table of n, a(n) for n = 1..10000</a>
%e A355710 2 is a term since A355583(2) = A355583(3) = 2.
%t A355710 s[n_] := Times @@ (1 + IntegerExponent[n, {2, 3, 5}]); Select[Range[500], s[#] == s[#+1] &]
%o A355710 (PARI) s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1) * (valuation(n, 5) + 1);
%o A355710 s1 = s(1); for(k = 2, 500, s2 = s(k); if(s1 == s2, print1(k-1,", ")); s1 = s2);
%Y A355710 Cf. A355583, A355709 (3-smooth analog).
%Y A355710 Subsequences: A355711, A355712.
%Y A355710 Similar sequences: A005237, A006049, A332386, A343819, A344312, A344313, A344314, A348345.
%K A355710 nonn
%O A355710 1,1
%A A355710 _Amiram Eldar_, Jul 15 2022