A366790 -id:A366790 - cp's OEIS frontend

A366789 Fully multiplicative with a(p) = oddpart(primepi(p)).

1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 5, 1, 3, 1, 3, 1, 7, 1, 1, 3, 1, 5, 9, 1, 9, 3, 1, 1, 5, 3, 11, 1, 5, 7, 3, 1, 3, 1, 3, 3, 13, 1, 7, 5, 3, 9, 15, 1, 1, 9, 7, 3, 1, 1, 15, 1, 1, 5, 17, 3, 9, 11, 1, 1, 9, 5, 19, 7, 9, 3, 5, 1, 21, 3, 9, 1, 5, 3, 11, 3, 1, 13, 23, 1, 21, 7, 5, 5, 3, 3, 3, 9, 11, 15, 3, 1, 25, 1, 5, 9

Offset: 1

Antti Karttunen, Oct 23 2023

Cf. A000265, A000720, A003963, A366790.

Cf. also A336466.

{1}~Join~Array[#/2^IntegerExponent[#, 2] &@ Apply[Times, PrimePi[#1]^#2 & @@@ FactorInteger[#]] &, 120, 2] (* Michael De Vlieger, Oct 23 2023 *)

A000265(n) = (n>>valuation(n,2));
A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };

a(n) = A000265(A003963(n)).

A366792 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365425(i) = A365425(j) and A366787(i) = A366787(j) for all i, j >= 0.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 2, 1, 8, 5, 9, 3, 10, 6, 3, 2, 11, 7, 7, 4, 12, 2, 13, 1, 14, 8, 15, 5, 16, 9, 5, 3, 17, 10, 11, 6, 18, 3, 19, 2, 20, 11, 10, 7, 21, 7, 22, 4, 18, 12, 23, 2, 22, 13, 4, 1, 24, 14, 25, 8, 26, 15, 8, 5, 27, 16, 20, 9, 28, 5, 29, 3, 30, 17, 17, 10, 31, 11, 32, 6, 33, 18, 34, 3

Offset: 0

Antti Karttunen, Oct 23 2023

Restricted growth sequence transform of the ordered pair [A365425(n), A366787(n)].
Restricted growth sequence transform of the function f(n) = A366790(A163511(n)).
For all i, j >= 0: a(i) = a(j) => A366788(i) = A366788(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A000265, A163511, A365425, A366787.

Cf. also A365394, A365395.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A365425(n) = A046523(A000265(A163511(n)));
A366789(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(primepi(f[k, 1]))^f[k, 2]); };
A366787(n) = A366789(A163511(n));
A366792aux(n) = [A365425(n), A366787(n)];
v366792 = rgs_transform(vector(1+up_to,n,A366792aux(n-1)));
A366792(n) = v366792[1+n];

For all n >= 1, a(n) = a(2*n) = a(A000265(n)).

cp's OEIS Frontend

A366789 Fully multiplicative with a(p) = oddpart(primepi(p)).

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