A319349 Filter sequence combining parity of n, A003557(n) and A051953(n).

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

Offset: 1

Author

Antti Karttunen, Sep 29 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of triple [A000035(n), A003557(n), A051953(n)], or equally, of triple [A007814(n), A003557(n), A051953(n)], or equally, of ordered pair [A000035(n), A319348(n)].

Links

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

Crossrefs

Cf. A000035, A003557, A007814, A051953, A305801, A319348.

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; };
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
A051953(n) = (n-eulerphi(n));
v319349 = rgs_transform(vector(up_to,n,[(n%2),A003557(n),A051953(n)]));
A319349(n) = v319349[n];

Formula

For n >= 3, a(n) = 1 + A319348(n).