A318891 Filter sequence combining the prime signature of n (A046523) with the largest prime factor of n (A006530).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 10, 15, 16, 12, 17, 18, 14, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 19, 30, 14, 31, 32, 33, 23, 34, 35, 36, 37, 38, 18, 39, 40, 41, 42, 18, 30, 43, 44, 21, 19, 45, 33, 46, 47, 48, 49, 50, 25, 51, 23, 52, 53, 54, 39, 36, 55, 56, 57, 58, 18, 59, 19, 60, 61, 62, 63, 64, 65, 66, 30, 67, 46, 68, 69, 48, 23, 70, 50

Offset: 1

Author

Antti Karttunen, Sep 16 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A286356.

For all i, j: a(i) = a(j) => A297112(i) = A297112(j). (Also, equivalently, A297113 or A297167 in place of A297112.)

Links

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

Crossrefs

Cf. A006530, A046523, A061395, A286356, A318890.

Cf. also A297112, A297113, A297167.

Programs

PARI

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A318891aux(n) = [A046523(n), A061395(n)];
v318891 = rgs_transform(vector(up_to,n,A318891aux(n)));
A318891(n) = v318891[n];