A305976 Filter sequence for a(prime^k) = constant sequences.

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

Offset

1,2

Links

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

Formula

a(1) = 1, for n > 1, if A010055(n) = 1 [when n is in A246655], a(n) = 2, otherwise a(n) = 2+A085970(n) = running count from 3 onward.

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); }
v065515 = partialsums(n -> (omega(n)<=1), up_to);
A065515(n) = v065515[n];
A085970(n) = (n - A065515(n));
A305976(n) = if(1==n, n, if(isprimepower(n), 2, 2+A085970(n)));

Crossrefs

Cf. A000961 (A246655), A085970, A305800, A305975, A305979.

Sequence in context: A326193 A327163 A324538 * A074592 A089993 A220431

Adjacent sequences: A305973 A305974 A305975 * A305977 A305978 A305979

Keyword

nonn

Author

Antti Karttunen, Jul 02 2018

Status

approved