A302039 Analog of A056239 for nonstandard factorization based on the sieve of Eratosthenes (A083221).

0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 6, 5, 5, 4, 7, 5, 8, 5, 6, 6, 9, 5, 6, 7, 6, 6, 10, 6, 11, 5, 7, 8, 7, 6, 12, 9, 7, 6, 13, 7, 14, 7, 8, 10, 15, 6, 8, 7, 8, 8, 16, 7, 9, 7, 8, 11, 17, 7, 18, 12, 8, 6, 8, 8, 19, 9, 9, 8, 20, 7, 21, 13, 9, 10, 9, 8, 22, 7, 9, 14, 23, 8, 10, 15, 9, 8, 24, 9, 12, 11, 10, 16, 9, 7, 25, 9, 10, 8, 26, 9, 27, 9, 10

Offset

1,3

Comments

Each n occurs A000041(n) times in total.

Links

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

Index entries for sequences generated by sieves

Formula

a(1) = 0; for n > 1, a(n) = A055396(n) + a(A302042(n)).

a(1) = 0; for n > 1, a(n) = (A055396(n)*A302045(n)) + a(A302044(n)).

a(n) = A056239(A250246(n)).

Prog

(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639, by Hasler.
A055396(n) = if(1==n, 0, primepi(A020639(n)));
v078898 = ordinal_transform(vector(up_to, n, A020639(n)));
A078898(n) = v078898[n];
A302042(n) = if((1==n)||isprime(n), 1, my(c = A078898(n), p = prime(-1+primepi(A020639(n))+primepi(A020639(c))), d = A078898(c), k=0); while(d, k++; if((1==k)||(A020639(k)>=p), d -= 1)); (k*p));
A302039(n) = if(1==n, 0, A055396(n) + A302039(A302042(n)));

Crossrefs

Cf. A000041, A056239, A250246, A302042, A302044, A302045.

Cf. also A253557, A302041, A302050, A302051, A302052, A302055 for other similar analogs.

Sequence in context: A226164 A366604 A308220 * A056239 A161511 A319856

Adjacent sequences: A302036 A302037 A302038 * A302040 A302041 A302042

Keyword

nonn

Author

Antti Karttunen, Mar 31 2018

Status

approved