A354095 a(n) = A354092(sigma(n)).

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

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

Cf. A000203, A007949, A010872, A354092, A354093, A354096.

Cf. also A350073.

Programs

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); };

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)).