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

1,2

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

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; };
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];

Crossrefs

Cf. A014197, A046523, A305801.

Cf. also A097946.

Sequence in context: A322024 A326203 A355835 * A322588 A323401 A326199

Adjacent sequences: A305893 A305894 A305895 * A305897 A305898 A305899

Keyword

nonn

Author

Antti Karttunen, Jul 01 2018

Status

approved