cp's OEIS Frontend

A302848 Permutation of natural numbers: a(1) = 1; for n > 1, a(n) = 1+A064989(A003961(n)-2).

%I A302848 #12 Dec 23 2024 14:53:45
%S A302848 1,2,3,6,4,12,5,10,20,18,8,42,7,30,15,74,14,72,11,60,48,32,9,86,44,26,
%T A302848 75,90,24,102,16,240,21,22,19,212,23,62,80,92,38,158,13,58,168,40,27,
%U A302848 320,66,70,59,150,35,368,84,160,110,56,54,312,34,108,111,720,45,192,39,122,78,228,68,662,36,50,33,112,87,134,17,328,416,114,47,300,128
%N A302848 Permutation of natural numbers: a(1) = 1; for n > 1, a(n) = 1+A064989(A003961(n)-2).
%H A302848 Antti Karttunen, <a href="/A302848/b302848.txt">Table of n, a(n) for n = 1..20000</a>
%H A302848 David Newman, et al., <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2018-January/018239.html">New sequences from old, Discussion on SeqFan-mailing list</a>, January 2018.
%H A302848 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A302848 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A302848 a(1) = 1; for n > 1, a(n) = 1+A064989(A003961(n)-2).
%F A302848 a(1) = 1; for n > 1, a(n) = 1+A064216(A048673(n)-1).
%o A302848 (PARI)
%o A302848 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A302848 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A302848 A302848(n) = if(1==n,n,1+A064989(A003961(n)-2));
%Y A302848 Cf. A302847 (inverse).
%Y A302848 Cf. A003961, A048673, A064216, A064989, A302850.
%K A302848 nonn
%O A302848 1,2
%A A302848 _Antti Karttunen_, Apr 26 2018