A319353 Filter sequence combining weights of partitions with Heinz-numbers equal to the proper divisors of n.

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

Offset: 1

Author

Antti Karttunen, Sep 17 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A319352.

For all i, j:

a(i) = a(j) => A301855(i) = A301855(j).

a(i) = a(j) => A304793(i) = A304793(j).

Links

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

Crossrefs

Cf. A056239, A319352.

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; };
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A319352(n) = { my(m=1); fordiv(n, d, if(dA056239(d)))); (m); };
v319353 = rgs_transform(vector(up_to,n,A319352(n)));
A319353(n) = v319353[n];