A354203 Fully multiplicative with a(p^e) = A354201(A000720(p))^e.

1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 7, 1, 5, 3, 2, 1, 13, 1, 11, 2, 3, 7, 19, 1, 4, 5, 1, 3, 17, 2, 23, 1, 7, 13, 6, 1, 29, 11, 5, 2, 37, 3, 31, 7, 2, 19, 43, 1, 9, 4, 13, 5, 41, 1, 14, 3, 11, 17, 47, 2, 53, 23, 3, 1, 10, 7, 59, 13, 19, 6, 67, 1, 61, 29, 4, 11, 21, 5, 71, 2, 1, 37, 79, 3, 26, 31, 17, 7, 73, 2, 15, 19, 23

Offset: 1

Author

Antti Karttunen, May 23 2022

Keywords

• nonn
• mult

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Left inverse of A354202.

Cf. A354201, A354206.

Programs

PARI

A354201(n) = if(n<=3,(n+1)\2,my(m=prime(n)%4); forstep(i=n-1,0,-1,if(m==(prime(i)%4),return(prime(i)))));
A354203(n) = { my(f=factor(n)); for(k=1,#f~,f[k,1] = A354201(primepi(f[k,1]))); factorback(f); };