A348747 Fully multiplicative with a(2) = 1, a(3) = 2, a(5) = 3, a(A002144(1+n)) = A002144(n) and a(A002145(1+n)) = a(A002145(1+n)) for all n >= 1, where A002144 and A002145 give the primes of the form 4k+1 and 4k+3 respectively.

1, 1, 2, 1, 3, 2, 7, 1, 4, 3, 11, 2, 5, 7, 6, 1, 13, 4, 19, 3, 14, 11, 23, 2, 9, 5, 8, 7, 17, 6, 31, 1, 22, 13, 21, 4, 29, 19, 10, 3, 37, 14, 43, 11, 12, 23, 47, 2, 49, 9, 26, 5, 41, 8, 33, 7, 38, 17, 59, 6, 53, 31, 28, 1, 15, 22, 67, 13, 46, 21, 71, 4, 61, 29, 18, 19, 77, 10, 79, 3, 16, 37, 83, 14, 39, 43, 34, 11, 73

Offset

1,3

Links

Table of n, a(n) for n=1..89.

Formula

Fully multiplicative with a(p) = A348745(A000720(p)).

a(A348746(n)) = n.

a(2n) = a(A000265(n)) = a(n).

Prog

(PARI) A348747(n) = { my(f=factor(n)); for(k=1, #f~, if(f[k, 1]<=3, f[k, 1]--, if(5==f[k, 1], f[k, 1]=3, if(1==(f[k, 1]%4), forstep(i=primepi(f[k, 1])-1, 0, -1, if(1==(prime(i)%4), f[k, 1]=prime(i); break)))))); factorback(f); };

Crossrefs

Left inverse of A348746.

Cf. A000265, A000720, A002144, A002145, A348745.

Cf. also A064989, A332819 for similar maps.

Sequence in context: A238944 A144238 A319622 * A082833 A101709 A005247

Adjacent sequences: A348744 A348745 A348746 * A348748 A348749 A348750

Keyword

nonn,mult

Author

Antti Karttunen, Nov 02 2021

Status

approved