A346486 a(1) = 1; for n > 1, a(n) = A020639(n) * a(A302044(n)).

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 3, 22, 23, 6, 5, 26, 21, 14, 29, 30, 31, 2, 15, 34, 35, 6, 37, 38, 33, 10, 41, 6, 43, 22, 3, 46, 47, 6, 7, 10, 15, 26, 53, 42, 5, 14, 21, 58, 59, 30, 61, 62, 39, 2, 55, 30, 67, 34, 15, 70, 71, 6, 73, 74, 51, 38, 77, 66, 79, 10, 33, 82, 83, 6, 35

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. A000265, A001221, A001222, A007947, A020639, A078898, A250246, A302041, A302044, A346487.

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; };
A000265(n) = (n/2^valuation(n, 2));
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1);
v078898 = ordinal_transform(vector(up_to,n,A020639(n)));
A078898(n) = v078898[n];
A302044(n) = { my(c = A000265(A078898(n))); if(1==c,1,my(p = prime(-1+primepi(A020639(n))+primepi(A020639(c))), d = A078898(c), k=0); while(d, k++; if((1==k)||(A020639(k)>=p),d -= 1)); (k*p)); };
A346486(n) = if(1==n,n,A020639(n)*A346486(A302044(n)));

Formula

a(1) = 1; and for n > 1, a(n) = A020639(n) * a(A302044(n)).

a(n) = A007947(A250246(n)) = A250246(n) / A346487(n).

For all n >= 1, A001221(a(n)) = A001222(a(n)) = A302041(n).