# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a339877 Showing 1-1 of 1 %I A339877 #8 Dec 25 2020 19:31:29 %S A339877 1,1,1,1,1,1,1,3,1,1,1,3,1,1,1,1,1,3,1,3,1,1,1,1,1,1,9,3,1,3,1,3,1,1, %T A339877 1,1,1,1,1,1,1,3,1,3,9,1,1,3,1,3,1,3,1,3,1,1,1,1,1,1,1,1,9,7,1,3,1,3, %U A339877 1,3,1,3,1,1,9,3,1,3,1,3,1,1,1,1,1,1,1,1,1,3,1,3,1,1,1,7,1,3,9,1,1,3,1,1,9 %N A339877 a(n) = A336467(A122111(n)). %H A339877 Antti Karttunen, Table of n, a(n) for n = 1..12166 %H A339877 Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537 %H A339877 Index entries for sequences computed from indices in prime factorization %F A339877 For noncomposite n, a(n) = 1, for composite n, a(n) = A000265(A105560(n)+1) * a(A064989(n)). %F A339877 a(n) = A336467(A122111(n)). %o A339877 (PARI) %o A339877 A000265(n) = (n>>valuation(n,2)); %o A339877 A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m)); %o A339877 A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); }; %o A339877 A339877(n) = A336467(A122111(n)); %o A339877 (PARI) %o A339877 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 A339877 A105560(n) = if(1==n,n,prime(bigomega(n))); %o A339877 A339877(n) = if(1==n||isprime(n),1,A000265(A105560(n)+1) * A339877(A064989(n))); %Y A339877 Cf. A000265, A064989, A105560, A122111, A336467. %Y A339877 Cf. also A339876, A334108. %K A339877 nonn %O A339877 1,8 %A A339877 _Antti Karttunen_, Dec 25 2020 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE