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.
%I A244414 #35 Nov 20 2022 01:55:14
%S A244414 1,2,3,4,5,1,7,8,9,10,11,2,13,14,15,16,17,3,19,20,21,22,23,4,25,26,27,
%T A244414 28,29,5,31,32,33,34,35,1,37,38,39,40,41,7,43,44,45,46,47,8,49,50,51,
%U A244414 52,53,9,55,56,57,58,59,10,61,62,63,64,65,11
%N A244414 Remove highest power of 6 from n.
%C A244414 This is instance g = 6 of the g-family of sequences, call it r(g,n), where for g >= 2 the highest power of g is removed from n. See the crossrefs.
%C A244414 The present sequence is not multiplicative: a(6) = 1 not a(2)*a(3) = 6. In the prime factor decomposition one has to consider a(2^e2*3^e^3) as one entity, also for e2 >= 0, e3 >= 0 with a(1) = 1, and apply the rule given in the formula section. With this rule the sequence will be multiplicative in an unusual sense. - _Wolfdieter Lang_, Feb 12 2018
%H A244414 Amiram Eldar, <a href="/A244414/b244414.txt">Table of n, a(n) for n = 1..10000</a>
%F A244414 a(n) = n/6^A122841(n), n >= 1.
%F A244414 For n >= 2, a(n) is sort of multiplicative if a(2^e2*3^e3) = 2^(e2 - m)*3^(e3 - m) with m = m(e2, e3) = min(e2, e3), for e2, e3 >= 0, a(1) = 1, and a(p^e) = p^e for primes p >= 5.
%F A244414 From _Peter Munn_, Jun 04 2020: (Start)
%F A244414 Proximity to being multiplicative may be expressed as follows:
%F A244414 a(n * A007310(k)) = a(n) * a(A007310(k));
%F A244414 a(n^2) = a(n)^2;
%F A244414 a(n) = a(A007913(n)) * a(A008833(n)).
%F A244414 (End)
%F A244414 Sum_{k=1..n} a(k) ~ (3/7) * n^2. - _Amiram Eldar_, Nov 20 2022
%e A244414 a(1) = 1 = 1/6^A122841(1) = 1/6^0.
%e A244414 a(9) = a(2^0*3^2), min(0,2) = 0, a(9) = 2^(0-0)*3^(2-0) = 1*9 = 9.
%e A244414 a(12) = a(2^2*3^1), m = min(2,1) = 1, a(12) = 2^(2-1)*3^(1-1) = 2^1*1 = 2.
%e A244414 a(30) = a(2*3*5) = a(2^1*3^1)*a(5) = 1*a(5) = 5.
%t A244414 a[n_] := n/6^IntegerExponent[n, 6]; Array[a, 66] (* _Robert G. Wilson v_, Feb 12 2018 *)
%o A244414 (PARI) a(n) = n/6^valuation(n,6); \\ _Joerg Arndt_, Jun 28 2014
%Y A244414 Cf. A122841, A000265, A038502, A065883, A132739, A242603.
%Y A244414 A007310, A007913, A008833 are used to express relationship between terms of this sequence.
%K A244414 nonn,easy
%O A244414 1,2
%A A244414 _Wolfdieter Lang_, Jun 27 2014
%E A244414 Incorrect multiplicity claim corrected by _Wolfdieter Lang_, Feb 12 2018