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A354095
a(n) = A354092(sigma(n)).
4
1, 3, 1, 7, 3, 3, 1, 6, 13, 9, 3, 7, 7, 3, 3, 31, 9, 39, 2, 21, 1, 9, 3, 6, 31, 21, 2, 7, 6, 9, 1, 63, 3, 27, 3, 91, 19, 6, 7, 18, 21, 3, 5, 21, 39, 9, 3, 31, 57, 93, 9, 49, 27, 6, 9, 6, 2, 18, 6, 21, 31, 3, 13, 127, 21, 9, 11, 63, 3, 9, 9, 78, 37, 57, 31, 14, 3, 21, 2, 93, 25, 63, 21, 7, 27, 15, 6, 18, 18, 117, 7
OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = A354092(1 + p + p^2 + ... + p^e).
a(n) = A354092(A000203(n)).
For all n >= 1, A010872(a(n)) = A010872(A354096(n)), A007949(a(n)) = A007949(A000203(n)).
PROG
(PARI) A354095(n) = { my(f=factor(sigma(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); };
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, May 17 2022
STATUS
approved