A354206 a(n) = A354203(sigma(A354202(n))), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)), and A354203 is its left inverse.

1, 1, 1, 23, 3, 1, 1, 5, 11, 3, 2, 23, 1, 1, 3, 469, 2, 11, 1, 69, 1, 2, 1, 5, 53, 1, 4, 23, 11, 3, 7, 69, 2, 2, 3, 253, 3, 1, 1, 15, 1, 1, 1, 46, 33, 1, 2, 469, 33, 53, 2, 23, 23, 4, 6, 5, 1, 11, 13, 69, 29, 7, 11, 19507, 3, 2, 1, 46, 1, 3, 2, 55, 2, 3, 53, 23, 2, 1, 3, 1407, 2797, 1, 5, 23, 6, 1, 11, 10, 9, 33

Offset

1,4

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

Multiplicative with a(p^e) = A354203((q^(e+1)-1)/(q-1)) where q = A354200(A000720(p)).

a(n) = A354203(A354205(n)) = A354203(sigma(A354202(n))).

a(n) = n - A354207(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); };
A354206(n) = A354203(sigma(A354202(n)));

Crossrefs

Cf. A000203, A000720, A354200, A354201, A354202, A354203, A354205, A354207.

Cf. A354361 (positions of 1's).

Cf. also A326042, A348750, A354088, A354096 for similar constructions.

Sequence in context: A051313 A350201 A040518 * A040517 A040519 A040520

Adjacent sequences: A354203 A354204 A354205 * A354207 A354208 A354209

Keyword

nonn,mult

Author

Antti Karttunen, May 23 2022

Status

approved