A318892 Filter sequence combining the prime signature of n (A046523) with A289625.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 35, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 44, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 68, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 75, 90

Offset: 1

Author

Antti Karttunen, Sep 16 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A289628.

For all i, j: a(i) = a(j) => A318893(i) = A318893(j).

Links

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

Crossrefs

Cf. A046523, A289625, A289628, A318839, A318893.

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
A289625(n) = { my(m=1,p=2,v=znstar(n)[2]); for(i=1,length(v),m *= p^v[i]; p = nextprime(p+1)); (m); };
A318892aux(n) = [A046523(n), A289625(n)];
v318892 = rgs_transform(vector(up_to,n,A318892aux(n)));
A318892(n) = v318892[n];