A354205 a(n) = sigma(A354202(n)), where A354202 is fully multiplicative with a(p) = A354200(A000720(p)).

1, 6, 8, 31, 14, 48, 12, 156, 57, 84, 20, 248, 18, 72, 112, 781, 30, 342, 24, 434, 96, 120, 32, 1248, 183, 108, 400, 372, 38, 672, 44, 3906, 160, 180, 168, 1767, 42, 144, 144, 2184, 54, 576, 48, 620, 798, 192, 60, 6248, 133, 1098, 240, 558, 62, 2400, 280, 1872, 192, 228, 68, 3472, 74, 264, 684, 19531, 252, 960, 72

Offset

1,2

Links

Table of n, a(n) for n=1..67.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

a(n) = A000203(A354202(n)).

a(n) = Sum_{d|n} A354202(d).

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))));
A354205(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = A354200(primepi(f[k, 1]))); sigma(factorback(f)); };
\\ Alternatively:
A354205(n) = sumdiv(n, d, A354202(d));

Crossrefs

Cf. A000203, A000290 (positions of odd terms), A000720, A354200, A354202, A354204, A354206.

Cf. A003973, A354089, A354093 for variants.

Sequence in context: A323201 A261062 A076904 * A219681 A025091 A356742

Adjacent sequences: A354202 A354203 A354204 * A354206 A354207 A354208

Keyword

nonn,mult

Author

Antti Karttunen, May 23 2022

Status

approved