A319709 Filter sequence combining primorial base representations of the proper divisors of n; Restricted growth sequence transform of A319708.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 4, 17, 18, 19, 2, 20, 2, 21, 22, 23, 18, 24, 2, 25, 26, 27, 2, 28, 2, 29, 30, 31, 2, 32, 33, 34, 12, 35, 2, 36, 37, 38, 39, 40, 2, 41, 2, 42, 43, 44, 45, 46, 2, 47, 48, 49, 2, 50, 2, 51, 52, 53, 45, 54, 2, 55, 56, 57, 2, 58, 59, 60, 61, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71

Offset

1,2

Comments

For all i, j:

a(i) = a(j) => A001065(i) = A001065(j),

a(i) = a(j) => A319713(i) = A319713(j).

Links

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

Prog

(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; };
A276086(n) = { my(i=0, m=1, pr=1, nextpr); while((n>0), i=i+1; nextpr = prime(i)*pr; if((n%nextpr), m*=(prime(i)^((n%nextpr)/pr)); n-=(n%nextpr)); pr=nextpr); m; };
A319708(n) = { my(m=1); fordiv(n, d, if(d<n, m *= A276086(d))); (m); };
v319709 = rgs_transform(vector(up_to, n, A319708(n)));
A319709(n) = v319709[n];

Crossrefs

Cf. A276086, A319708, A319713.

Cf. A293215, A293226, A300835 for similar constructions for other bases.

Sequence in context: A353523 A293217 A329351 * A293226 A328315 A327970

Adjacent sequences: A319706 A319707 A319708 * A319710 A319711 A319712

Keyword

nonn

Author

Antti Karttunen, Oct 03 2018

Status

approved