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a(n) = A005940(1+A324104(n)); Euler totient phi conjugated by A156552.
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%I #6 Mar 18 2021 22:58:25

%S 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 23,25,29,81,11,385,7,21,31,23,35,49,37,55,41,39,15,1105,43,135,7,35,

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(1) = 1, and for n > 1, a(n) = A005940(1+A000010(A156552(n))).

%F a(n) = A005940(1+A324104(n)).

%F For n >= 2, a(A000040(n)) = A000040(n-1).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o 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 A324104(n) = if(1==n,0,eulerphi(A156552(n)));

%o A342654(n) = A005940(1+A324104(n));

%Y Cf. A000010, A005940, A156552, A324104.

%Y Cf. also A332223 (sigma similarly conjugated).

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 18 2021