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

Author

Antti Karttunen, May 23 2022

Keywords

• nonn
• mult

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Cf. A003973, A354089, A354093 for variants.

Programs

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));

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).