A318893 Filter sequence combining the prime signature of n (A046523) with Euler totient function (A000010).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 21, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 34, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 42, 48, 43, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 53, 70, 59, 71, 66, 72, 73, 74, 51, 75, 76, 77, 78, 79, 80, 81, 76, 82, 83, 71

Offset: 1

Author

Antti Karttunen, Sep 16 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A286160.

For all i, j: a(i) = a(j) => A062355(i) = A062355(j).

Links

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

Crossrefs

Cf. A000010, A046523, A286160, A318839, A318892.

Cf. also A061468, A062355.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A318893aux(n) = [eulerphi(n), A046523(n)];
v318893 = rgs_transform(vector(up_to,n,A318893aux(n)));
A318893(n) = v318893[n];