A305983 Filter sequence combining from all proper divisors d of n, the prime signature of 2d+1.

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

Offset: 1

Author

Antti Karttunen, Jun 15 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A305982.

For all i, j: a(i) = a(j) => A305818(i) = A305818(j).

Links

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

Crossrefs

Cf. A305973, A305982, A305985.

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; };
A305982(n) = { my(m=1); fordiv(n, d, if((dA305973(1+d)-1))); (m); }; \\ Needs also code from A305973.
v305983 = rgs_transform(vector(up_to,n,A305982(n)));
A305983(n) = v305983[n];