A346487 a(n) = A003557(A250246(n)).

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 9, 1, 1, 4, 5, 1, 1, 2, 1, 1, 1, 16, 3, 1, 1, 6, 1, 1, 1, 4, 1, 9, 1, 2, 27, 1, 1, 8, 7, 5, 5, 2, 1, 1, 25, 4, 3, 1, 1, 2, 1, 1, 1, 32, 1, 3, 1, 2, 9, 1, 1, 12, 1, 1, 1, 2, 1, 1, 1, 8, 3, 1, 1, 18, 5, 1, 1, 4, 1, 27, 49, 2, 81, 1, 1, 16, 1, 7, 1, 10, 1, 5, 1, 4, 15

Offset: 1

Author

Antti Karttunen, Aug 17 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences generated by sieves

Crossrefs

Cf. A003557, A083221, A250246, A346486.

Programs

PARI

up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
A055396(n) = if(1==n,0,primepi(A020639(n)));
v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
A078898(n) = v078898[n];
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A250246(n) = if(1==n,n,my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A346487(n) = A003557(A250246(n));

Formula

a(n) = A003557(A250246(n)) = A250246(n) / A346486(n).

For all primes p, a(p) = 1.