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A354093
a(n) = sigma(A354091(n)), where A354091 is fully multiplicative prime shift which replaces the primes of the form 3k+2 by the next larger such prime, while other primes stay as they are, and sigma is the sum of divisors function.
6
1, 6, 4, 31, 12, 24, 8, 156, 13, 72, 18, 124, 14, 48, 48, 781, 24, 78, 20, 372, 32, 108, 30, 624, 133, 84, 40, 248, 42, 288, 32, 3906, 72, 144, 96, 403, 38, 120, 56, 1872, 48, 192, 44, 558, 156, 180, 54, 3124, 57, 798, 96, 434, 60, 240, 216, 1248, 80, 252, 72, 1488, 62, 192, 104, 19531, 168, 432, 68, 744, 120, 576
OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = (q^(e+1)-1)/(q-1) where q = A003627(1+n) if p = A003627(n), otherwise q = p.
a(n) = Sum_{d|n} A354091(d).
For all n >= 1, A010872(a(n)) = A010872(A000203(n)) = A074941(n).
PROG
(PARI) A354093(n) = { my(f=factor(n)); for(k=1, #f~, if(2==(f[k, 1]%3), for(i=1+primepi(f[k, 1]), oo, if(2==(prime(i)%3), f[k, 1]=prime(i); break)))); sigma(factorback(f)); };
CROSSREFS
Inverse Möbius transform of A354091.
Cf. A003973, A354089 for variants.
Sequence in context: A191567 A274707 A372524 * A377018 A163934 A163939
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 17 2022
STATUS
approved