A305985 Filter sequence combining from all divisors d > 1 of n, the prime signature of 2d+1.

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

Offset: 1

Author

Antti Karttunen, Jun 15 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A305984.

For all i, j: a(i) = a(j) => A086668(i) = A086668(j).

Links

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

Crossrefs

Cf. A305810, A305973, A305983, A305984.

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; };
A305984(n) = { my(m=1); fordiv(n, d, if((d>1), m *= prime(A305973(1+d)-1))); (m); }; \\ Needs also code from A305973.
v305985 = rgs_transform(vector(up_to,n,A305984(n)));
A305985(n) = v305985[n];