A227183 -id:A227183 - cp's OEIS frontend

A227752 a(n) is the number of occurrences of n in A226062.

1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 3, 1, 0, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0

Offset: 0

Antti Karttunen, Jul 26 2013

nonn

Antti Karttunen, Table of n, a(n) for n = 0..319

A227753 gives the positions of zeros.

In the following formula [] stands for Iverson brackets. Essentially we are just naively counting the integers which A226062 maps to n. A000225 is the guaranteed upper limit for the runlength codes for the partitions of size n:
a(n) = Sum_{i=0..A000225(A227183(n))} [A226062(i)==n].
a(n) = Sum_{i=A227368(A227183(n))..A000225(A227183(n))} [A226062(i)==n]. [This is slightly faster if somebody invents a clever formula for the lower limit A227368.]

A322825 A variant of A322827.

Original entry on oeis.org

1, 2, 6, 4, 36, 30, 18, 8, 216, 450, 210, 900, 108, 150, 54, 16, 1296, 6750, 7350, 13500, 44100, 2310, 22050, 27000, 648, 2250, 1470, 4500, 324, 750, 162, 32, 7776, 101250, 257250, 202500, 1543500, 177870, 771750, 405000, 9261000, 2668050, 30030, 5336100, 4630500, 889350, 2315250, 810000, 3888, 33750, 51450, 67500

Offset: 0

Antti Karttunen, Jan 16 2019

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A005811, A227183, A322827 (the main entry).

A322825(n) = if(!n,1, my(rl=1, m=1, p=2, eb = (n%2)); n>>=1; while(n,if((n%2)==eb, rl++, eb = 1-eb; m *= p^rl; p = nextprime(1+p)); n >>= 1); m *= p^rl; (m));

A322825(n) = if(!n,1,my(bits = Vecrev(binary(n)), rl=1, o = List([])); for(i=2,#bits,if(bits[i]==bits[i-1], rl++, listput(o,rl))); listput(o,rl); my(es=Vec(o), m=1); for(i=1,#es,m *= prime(i)^es[i]); (m));

A001221(a(n)) = A005811(n).
A001222(a(n)) = A227183(n).
A046523(a(n)) = A322827(n).

cp's OEIS Frontend

A227752 a(n) is the number of occurrences of n in A226062.

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