cp's OEIS Frontend

A332817 a(n) = A108548(A163511(n)).

%I A332817 #11 Mar 10 2020 00:29:04
%S A332817 1,2,4,3,8,9,6,5,16,27,18,25,12,15,10,7,32,81,54,125,36,75,50,49,24,
%T A332817 45,30,35,20,21,14,13,64,243,162,625,108,375,250,343,72,225,150,245,
%U A332817 100,147,98,169,48,135,90,175,60,105,70,91,40,63,42,65,28,39,26,11,128,729,486,3125,324,1875,1250,2401,216,1125,750,1715,500
%N A332817 a(n) = A108548(A163511(n)).
%C A332817 This irregular table can be represented as a binary tree. Each child to the left is obtained by doubling the parent, and each child to the right is obtained by applying A332818 to the parent:
%C A332817                                        1
%C A332817                                        |
%C A332817                     ...................2...................
%C A332817                    4                                       3
%C A332817          8......../ \........9                   6......../ \........5
%C A332817         / \                 / \                 / \                 / \
%C A332817        /   \               /   \               /   \               /   \
%C A332817       /     \             /     \             /     \             /     \
%C A332817     16       27         18       25         12       15         10       7
%C A332817   32 81    54  125    36  75   50  49     24  45   30  35     20  21   14 13
%C A332817 etc.
%C A332817 This is the mirror image of the tree in A332815.
%H A332817 Antti Karttunen, <a href="/A332817/b332817.txt">Table of n, a(n) for n = 0..16383</a>
%H A332817 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A332817 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A332817 a(n) = A108548(A163511(n)).
%F A332817 For n >= 1, a(n) = A332815(A054429(n)).
%o A332817 (PARI)
%o A332817 up_to = 26927;
%o A332817 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A332817 A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
%o A332817 A163511(n) = if(!n,1,A005940(1+A054429(n)));
%o A332817 A108546list(up_to) = { my(v=vector(up_to), p,q); v[1] = 2; v[2] = 3; v[3] = 5; for(n=4,up_to, p = v[n-2]; q = nextprime(1+p); while(q%4 != p%4, q=nextprime(1+q)); v[n] = q); (v); };
%o A332817 v108546 = A108546list(up_to);
%o A332817 A108546(n) = v108546[n]; \\ _Antti Karttunen_, Mar 05 2020
%o A332817 A108548(n) = { my(f=factor(n)); f[,1] = apply(A108546,apply(primepi,f[,1])); factorback(f); };
%o A332817 A332817(n) = A108548(A163511(n));
%Y A332817 Cf. A332811 (inverse permutation).
%Y A332817 Cf. A054429, A108548, A163511, A332815 (mirror image).
%Y A332817 Cf. A108546 (the right edge of the tree from 2 downward).
%Y A332817 Cf. also A332214.
%K A332817 nonn,tabf
%O A332817 0,2
%A A332817 _Antti Karttunen_, Mar 05 2020