A354089 Sum of divisors function applied to Pythagorean prime shift: a(n) = sigma(A348746(n)).

1, 4, 6, 13, 14, 24, 8, 40, 31, 56, 12, 78, 18, 32, 84, 121, 30, 124, 20, 182, 48, 48, 24, 240, 183, 72, 156, 104, 38, 336, 32, 364, 72, 120, 112, 403, 42, 80, 108, 560, 54, 192, 44, 156, 434, 96, 48, 726, 57, 732, 180, 234, 62, 624, 168, 320, 120, 152, 60, 1092, 74, 128, 248, 1093, 252, 288, 68, 390, 144, 448, 72

Offset: 1

Author

Antti Karttunen, May 17 2022

Keywords

• nonn
• mult

Links

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

Crossrefs

Inverse Möbius transform of A348746.

Cf. A000203, A000720, A348744, A354088.

Cf. A003973, A354093 for variants.

Programs

PARI

A348746(n) = { my(f=factor(n)); for(k=1,#f~, if(2==f[k,1], f[k,1]=3, if(3==f[k,1], f[k,1]=5, if(1==(f[k,1]%4), for(i=1+primepi(f[k,1]),oo,if(1==(prime(i)%4), f[k,1]=prime(i); break)))))); factorback(f); };
A354089(n) = sigma(A348746(n));

Formula

Multiplicative with a(p^e) = (q^(e+1)-1)/(q-1) where q = A348744(A000720(p)).

a(n) = A000203(A348746(n)).

a(n) = Sum_{d|n} A348746(d).