A347376 - OEIS

%I #11 Nov 03 2021 22:31:33

%S 1,2,4,6,6,8,10,12,20,18,12,12,16,26,24,24,18,16,22,24,40,48,28,24,42,

%T 56,40,36,30,24,36,48,68,78,60,36,40,86,74,48,42,32,46,60,60,104,52,

%U 48,110,78,102,72,58,68,72,72,118,138,60,48,66,144,80,96,96,52,70,96,142,84,72,72,78,176,108,108,120,70

%N Möbius transform of A250469.

%C Question: Are all terms positive?

%H Antti Karttunen, <a href="/A347376/b347376.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%F a(n) = Sum_{d|n} A008683(n/d) * A250469(d).

%F a(n) = A003972(n) - A347377(n).

%o (PARI)

%o up_to = 10000;

%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };

%o A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639

%o v078898 = ordinal_transform(vector(up_to,n,A020639(n)));

%o A078898(n) = v078898[n];

%o A250469(n) = if(1==n,n,my(spn = nextprime(1+A020639(n)), c = A078898(n), k = 0); while(c, k++; if((1==k)||(A020639(k)>=spn),c -= 1)); (k*spn));

%o A347376(n) = sumdiv(n,d,moebius(n/d)*A250469(d));

%Y Cf. A003972, A008683, A020639, A078898, A250469, A347377.

%Y Cf. also A346479.

%K nonn

%O 1,2

%A _Antti Karttunen_, Sep 01 2021