A354089 - OEIS

%I #9 May 17 2022 17:50:09

%S 1,4,6,13,14,24,8,40,31,56,12,78,18,32,84,121,30,124,20,182,48,48,24,

%T 240,183,72,156,104,38,336,32,364,72,120,112,403,42,80,108,560,54,192,

%U 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

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

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

%o (PARI)

%o 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); };

%o A354089(n) = sigma(A348746(n));

%Y Inverse Möbius transform of A348746.

%Y Cf. A000203, A000720, A348744, A354088.

%Y Cf. A003973, A354093 for variants.

%K nonn,mult

%O 1,2

%A _Antti Karttunen_, May 17 2022