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

1,2

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

Formula

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

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; };
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];

Crossrefs

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

Sequence in context: A323370 A323405 A353521 * A353520 A361021 A322973

Adjacent sequences: A319346 A319347 A319348 * A319350 A319351 A319352

Keyword

nonn

Author

Antti Karttunen, Sep 29 2018

Status

approved