cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A348568 Highly composite numbers (A002182) such that the exponents of 2 and 3 in their prime factorization are equal.

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%I A348568 #66 Oct 14 2022 08:53:36
%S A348568 1,6,36,180,1260,7560,45360,83160,498960,1081080,6486480,32432400,
%T A348568 110270160,551350800,2095133040,10475665200,73329656400,240940299600,
%U A348568 1686582097200,48910880818800,1516237305382800
%N A348568 Highly composite numbers (A002182) such that the exponents of 2 and 3 in their prime factorization are equal.
%C A348568 These are all the terms in the sequence because for a number x that has exponents of 2 and 3 equal and >= 5 in its prime factorization, 8x/9 is a smaller number with at least the same number of divisors. Since 1516237305382800 is the greatest highly composite number that is not a multiple of 32, A134592(32), it is the last term of this sequence.
%F A348568 Intersection of A002182 and A064615.
%e A348568 1516237305382800 is highly composite and its prime factorization is 2^4 * 3^4 * 5^2 * 7^2 * 11 * 13 * 17 * 19 * 23 * 29 * 31. Since the exponents of 2 and 3 are both 4, 1516237305382800 is in this sequence.
%t A348568 HCN = Import["https://oeis.org/A002182/b002182.txt", "Table"][[;; , 2]]; Select[HCN, IntegerExponent[#, 2] == IntegerExponent[#, 3] &] (* _Amiram Eldar_, Oct 27 2021 *)
%Y A348568 Cf. A000005, A002182, A064615, A134592.
%K A348568 nonn,fini,full
%O A348568 1,2
%A A348568 _Tejo Vrush_, Oct 27 2021