A336157 -id:A336157 - cp's OEIS frontend

A336158 The least number with the prime signature of the odd part of n: a(n) = A046523(A000265(n)).

1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 2, 2, 6, 1, 2, 4, 2, 2, 6, 2, 2, 2, 4, 2, 8, 2, 2, 6, 2, 1, 6, 2, 6, 4, 2, 2, 6, 2, 2, 6, 2, 2, 12, 2, 2, 2, 4, 4, 6, 2, 2, 8, 6, 2, 6, 2, 2, 6, 2, 2, 12, 1, 6, 6, 2, 2, 6, 6, 2, 4, 2, 2, 12, 2, 6, 6, 2, 2, 16, 2, 2, 6, 6, 2, 6, 2, 2, 12, 6, 2, 6, 2, 6, 2, 2, 4, 12, 4, 2, 6, 2, 2, 30

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A001227, A005087, A046523, A064989, A087436, A336156, A336157, A336159, A336160.

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
A336158(n) = A046523(A000265(n));

from math import prod
from sympy import factorint, prime
def A336158(n): return prod(prime(i+1)**e for i,e in enumerate(sorted(factorint(n>>(~n&n-1).bit_length()).values(),reverse=True))) # Chai Wah Wu, Sep 16 2022

a(n) = A046523(A000265(n)) = A046523(A064989(n)).
A000005(a(n)) = A001227(n).
A001221(a(n)) = A005087(n).
A001222(a(n)) = A087436(n).

A336159 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 11 2020

Restricted growth sequence transform of the ordered pair [A278222(n), A336158(n)], i.e., of the ordered pair [A046523(A005940(1+n)), A046523(A000265(n))].

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000265, A005940, A046523, A278222, A336158.

Cf. also A003602, A286163, A286622, A291762, A324400, A336149, A336156, A336157, A336160, A336162.

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));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
A336158(n) = A046523(A000265(n));
Aux336159(n) = [A278222(n), A336158(n)];
v336159 = rgs_transform(vector(up_to, n, Aux336159(n)));
A336159(n) = v336159[n];

cp's OEIS Frontend

A336158 The least number with the prime signature of the odd part of n: a(n) = A046523(A000265(n)).

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