A354092 Fully multiplicative prime shift where the primes of the form 3k+2 are replaced by the previous such prime (with 2 -> 1), and primes of the form 3k and 3k+1 stay as they are.

1, 1, 3, 1, 2, 3, 7, 1, 9, 2, 5, 3, 13, 7, 6, 1, 11, 9, 19, 2, 21, 5, 17, 3, 4, 13, 27, 7, 23, 6, 31, 1, 15, 11, 14, 9, 37, 19, 39, 2, 29, 21, 43, 5, 18, 17, 41, 3, 49, 4, 33, 13, 47, 27, 10, 7, 57, 23, 53, 6, 61, 31, 63, 1, 26, 15, 67, 11, 51, 14, 59, 9, 73, 37, 12, 19, 35, 39, 79, 2, 81, 29, 71, 21, 22, 43, 69, 5, 83

Offset: 1

Author

Antti Karttunen, May 17 2022

Keywords

• nonn
• mult

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Left inverse of A354091.

Cf. A003627, A007645.

Cf. A064989, A348747 (variants).

Programs

PARI

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); };

Formula

Fully multiplicative with a(2) = 1, a(A003627(1+n)) = A003627(n), a(A007645(n)) = A007645(n).

For all n >= 1, a(A354091(n)) = n.