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A354096
a(n) = A354092(sigma(A354091(n))).
5
1, 3, 1, 31, 3, 3, 1, 39, 13, 9, 9, 31, 7, 3, 3, 295, 3, 39, 2, 93, 1, 27, 6, 39, 133, 21, 2, 31, 21, 9, 1, 1953, 9, 9, 3, 403, 19, 6, 7, 117, 3, 3, 5, 279, 39, 18, 27, 295, 57, 399, 3, 217, 6, 6, 27, 39, 2, 63, 9, 93, 31, 3, 13, 19531, 21, 27, 11, 93, 6, 9, 21, 507, 37, 57, 133, 62, 9, 21, 2, 885, 25, 9, 18, 31, 9
OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = A354092((q^(e+1)-1)/(q-1)), where q = A003627(1+n) if p = A003627(n), otherwise q = p.
For all n >= 1, A010872(a(n)) = A010872(A354095(n)).
For all k in A329963, A007949(a(k)) = A007949(sigma(k)) = A354100(k) = 0.
PROG
(PARI)
A354091(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)))); factorback(f); };
A354092(n) = { my(f=factor(n)); for(k=1, #f~, if(2==(f[k, 1]%3), if(2==f[k, 1], f[k, 1]--, forstep(i=primepi(f[k, 1])-1, 0, -1, if(2==(prime(i)%3), f[k, 1]=prime(i); break))))); factorback(f); };
A354096(n) = A354092(sigma(A354091(n)));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 17 2022
STATUS
approved