A354207 a(n) = n - A354203(sigma(A354202(n))), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)), and A354203 is its left inverse.
0, 1, 2, -19, 2, 5, 6, 3, -2, 7, 9, -11, 12, 13, 12, -453, 15, 7, 18, -49, 20, 20, 22, 19, -28, 25, 23, 5, 18, 27, 24, -37, 31, 32, 32, -217, 34, 37, 38, 25, 40, 41, 42, -2, 12, 45, 45, -421, 16, -3, 49, 29, 30, 50, 49, 51, 56, 47, 46, -9, 32, 55, 52, -19443, 62, 64, 66, 22, 68, 67, 69, 17, 71, 71, 22, 53, 75, 77, 76
Offset: 1
Keywords
Links
Programs
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PARI
A354200(n) = if(1==n,5,my(p=prime(n), m=p%4); forprime(q=1+p,,if(m==(q%4),return(q)))); A354201(n) = if(n<=3,(n+1)\2,my(m=prime(n)%4); forstep(i=n-1,0,-1,if(m==(prime(i)%4),return(prime(i))))); A354202(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354200(primepi(f[k,1]))); factorback(f); }; A354203(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354201(primepi(f[k,1]))); factorback(f); }; A354207(n) = (n-A354203(sigma(A354202(n))));
Formula
a(n) = n - A354206(n).