cp's OEIS Frontend

A342654 a(n) = A005940(1+A324104(n)); Euler totient phi conjugated by A156552.

%I A342654 #6 Mar 18 2021 22:58:25
%S A342654 1,2,2,3,3,5,5,9,3,9,7,15,11,11,5,7,13,25,17,21,9,35,19,45,5,121,9,49,
%T A342654 23,25,29,81,11,385,7,21,31,23,35,49,37,55,41,39,15,1105,43,135,7,35,
%U A342654 121,51,47,125,25,99,385,4693,53,105,59,85085,21,55,13,175,61,5929,23,77,67,77,71,279841,25,8281,11,1225
%N A342654 a(n) = A005940(1+A324104(n)); Euler totient phi conjugated by A156552.
%H A342654 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A342654 a(1) = 1, and for n > 1, a(n) = A005940(1+A000010(A156552(n))).
%F A342654 a(n) = A005940(1+A324104(n)).
%F A342654 For n >= 2, a(A000040(n)) = A000040(n-1).
%o A342654 (PARI)
%o A342654 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A342654 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
%o A342654 A324104(n) = if(1==n,0,eulerphi(A156552(n)));
%o A342654 A342654(n) = A005940(1+A324104(n));
%Y A342654 Cf. A000010, A005940, A156552, A324104.
%Y A342654 Cf. also A332223 (sigma similarly conjugated).
%K A342654 nonn
%O A342654 1,2
%A A342654 _Antti Karttunen_, Mar 18 2021