A347117 - OEIS

%I #9 Nov 03 2021 22:31:16

%S 2,3,6,10,16,0,48,30,12,104,96,12,240,192,8,90,336,54,576,240,16,504,

%T 720,36,24,600,40,480,1056,-122,1680,270,96,1104,96,132,1920,1224,144,

%U 720,2736,1064,3360,1200,0,1920,3696,108,60,126,624,1680,4416,422,336,1440,768,3144,5616,-228,6960,3120,416,810,624

%N Möbius transform of A329603.

%H Antti Karttunen, <a href="/A347117/b347117.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = Sum_{d|n} A008683(n/d) * A329603(d).

%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 A329603(n) = A005940(2+(3*A156552(n)));

%o A347117(n) = sumdiv(n,d,moebius(n/d)*A329603(d));

%Y Cf. A008683, A156552, A329603.

%Y Cf. also A332463, A347115, A347118.

%K sign

%O 1,1

%A _Antti Karttunen_, Aug 21 2021