A319994 Let g = A006530(n), the largest prime factor of n. This filter sequence combines (g mod 4), n/g (A052126), and a single bit A319988(n) telling whether the largest prime factor is unitary.

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

Offset: 1

Author

Antti Karttunen, Oct 05 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of triple [A010873(A006530(n)), A052126(n), A319988(n)], with a separate value allotted for a(1).

Here among the first 100000 terms, only 2331 have a unique value, compared to 69714 in A320004.

For all i, j:

a(i) = a(j) => A024362(i) = A024362(j),

a(i) = a(j) => A067029(i) = A067029(j),

a(i) = a(j) => A071178(i) = A071178(j),

a(i) = a(j) => A077462(i) = A077462(j) => A101296(i) = A101296(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A006530, A052126, A319988, A320004.

Cf. also A319996 (modulo 6 analog).

Programs

PARI

up_to = 100000;
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; };
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A052126(n) = (n/A006530(n));
A319988(n) = ((n>1)&&(factor(n)[omega(n),2]>1));
A319994aux(n) = if(1==n,0,[A006530(n)%4, A052126(n), A319988(n)]);
v319994 = rgs_transform(vector(up_to,n,A319994aux(n)));
A319994(n) = v319994[n];