A305975 Filter sequence: All prime powers p^k, k >= 1, are allotted to distinct equivalence classes according to their exponent k, while all other numbers occur in singular equivalence classes of their own.

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

Offset

1,2

Comments

Restricted growth sequence transform of A305974.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j) => A305976(i) = A305976(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

a(prime) = 2, a(prime^2) = 3, a(prime^3) = 5, a(prime^4) = 10, a(prime^5) = 19.

Prog

(PARI)
up_to = 100000;
partialsums(f, up_to) = { my(v = vector(up_to), s=0); for(i=1, up_to, s += f(i); v[i] = s); (v); }
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; };
v065515 = partialsums(n -> (omega(n)<=1), up_to);
A065515(n) = v065515[n];
A085970(n) = (n - A065515(n));
A305974(n) = if(1==n, n, my(e = isprimepower(n)); if(e, -e, 1+A085970(n)));
v305975 = rgs_transform(vector(up_to, n, A305974(n)));
A305975(n) = v305975[n];

Crossrefs

Cf. A000961 (A246655), A085970, A305800, A305974, A305976, A305979.

Sequence in context: A300248 A300247 A318887 * A304751 A117658 A371446

Adjacent sequences: A305972 A305973 A305974 * A305976 A305977 A305978

Keyword

nonn

Author

Antti Karttunen, Jul 02 2018

Status

approved