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

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = n - A354206(n).

Prog

(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))));

Crossrefs

Cf. A000203, A354200, A354201, A354202, A354203, A354205, A354206.

Cf. also A348736.

Sequence in context: A321340 A221229 A221602 * A358980 A092120 A059706

Adjacent sequences: A354204 A354205 A354206 * A354208 A354209 A354210

Keyword

sign

Author

Antti Karttunen, May 23 2022

Status

approved