A319697 -id:A319697 - cp's OEIS frontend

A319698 Filter sequence combining A003557(n) [n divided by largest squarefree divisor of n] with A319697(n) [sum of even squarefree divisors of n].

1, 2, 1, 3, 1, 4, 1, 5, 6, 7, 1, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 14, 15, 16, 17, 18, 1, 19, 1, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26, 6, 19, 1, 27, 28, 29, 1, 30, 1, 31, 1, 32, 1, 33, 1, 34, 1, 25, 6, 35, 1, 36, 1, 37, 1, 36, 1, 38, 1, 39, 15, 40, 1, 41, 1, 42, 43, 44, 1, 45, 1, 46, 1, 47, 1, 48, 1, 34, 1, 36, 1, 49, 1, 50, 6, 51, 1, 52, 1, 53, 1

Offset: 1

Antti Karttunen, Oct 31 2018

nonn

Restricted growth sequence transform of ordered pair [A003557(n), A319697(n)].

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

Cf. A003557, A319697.

Cf also A291750, A291751.

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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A319697(n) = sumdiv(n, d, (!(d%2))*issquarefree(d)*d);
v319698 = rgs_transform(vector(up_to,n,[A003557(n),A319697(n)]));
A319698(n) = v319698[n];

A322022 Lexicographically earliest such sequence a that a(i) = a(j) => A305891(i) = A305891(j) and A319697(i) = A319697(j), for all i, j.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 11, 15, 3, 16, 7, 17, 18, 19, 3, 20, 3, 21, 11, 22, 11, 23, 3, 24, 11, 25, 3, 26, 3, 27, 28, 29, 3, 30, 7, 31, 11, 32, 3, 33, 11, 34, 11, 35, 3, 36, 3, 37, 28, 38, 11, 39, 3, 40, 11, 39, 3, 41, 3, 42, 28, 43, 11, 44, 3, 45, 46, 47, 3, 48, 11, 49, 11, 50, 3, 51, 11, 52, 11, 53, 11, 54, 3, 55, 28

Offset: 1

Antti Karttunen, Nov 29 2018

nonn

Restricted growth sequence transform of the ordered pair [A305891(n), A319697(n)], or equally, of the triple [A007814(n), A046523(n), A319697(n)].

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

Cf. A007814, A046523, A097272, A305891, A319697, A319698, A322021.

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; };
A007814(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
A319697(n) = sumdiv(n, d, (!(d%2))*issquarefree(d)*d);
v322022 = rgs_transform(vector(up_to, n, [A007814(n), A046523(n), A319697(n)]));
A322022(n) = v322022[n];

A323238 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A291750(n) for all n, except for odd numbers n > 1, f(n) = 0.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 10, 3, 11, 3, 12, 3, 13, 3, 14, 3, 15, 3, 16, 3, 17, 3, 18, 3, 19, 3, 20, 3, 21, 3, 22, 3, 23, 3, 24, 3, 17, 3, 25, 3, 26, 3, 27, 3, 28, 3, 29, 3, 30, 3, 31, 3, 23, 3, 32, 3, 33, 3, 34, 3, 33, 3, 35, 3, 36, 3, 37, 3, 38, 3, 39, 3, 40, 3, 41, 3, 42, 3, 43, 3, 44, 3, 31, 3, 33, 3, 45, 3, 46, 3, 47, 3, 48, 3, 49, 3

Offset: 1

Antti Karttunen, Jan 08 2019

nonn

For all i, j:
  A319701(i) = A319701(j) => a(i) = a(j),
  a(i) = a(j) => A146076(i) = A146076(j),
  a(i) = a(j) => A319697(i) = A319697(j).

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

Cf. A003557, A048250, A146076, A291750, A291751, A319698, A319697, A319701, A322588, A323237, A323241.

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; };
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
Aux323238(n) = if((n>1)&&(n%2),0,(1/2)*(2 + ((A003557(n)+A048250(n))^2) - A003557(n) - 3*A048250(n)));
v323238 = rgs_transform(vector(up_to, n, Aux323238(n)));
A323238(n) = v323238[n];

cp's OEIS Frontend

A319698 Filter sequence combining A003557(n) [n divided by largest squarefree divisor of n] with A319697(n) [sum of even squarefree divisors of n].

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A322022 Lexicographically earliest such sequence a that a(i) = a(j) => A305891(i) = A305891(j) and A319697(i) = A319697(j), for all i, j.

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A323238 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A291750(n) for all n, except for odd numbers n > 1, f(n) = 0.

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