A305896 Filter sequence combining prime signature of n (A046523) and the cardinality of invphi (A014197).

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

Offset: 1

Author

Antti Karttunen, Jul 01 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of ordered pair [A046523(n), A014197(n)].

For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A097946(i) = A097946(j).

Links

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

Crossrefs

Cf. A014197, A046523, A305801.

Cf. also A097946.

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; };
A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))} \\ This function from M. F. Hasler, Oct 05 2009
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux305896(n) = [A046523(n), A014197(n)];
v305896 = rgs_transform(vector(up_to, n, Aux305896(n)));
A305896(n) = v305896[n];