A302052 Characteristic function for A302053; an analog of A010052 (char. fun of squares) for the nonstandard factorization based on the sieve of Eratosthenes (A083221).

1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences generated by sieves

Formula

a(0) = 1, for n >= 1, a(n) = A302051(n) mod 2.

For n >= 1, a(n) = A010052(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.
v078898 = ordinal_transform(vector(up_to, n, A020639(n)));
A078898(n) = v078898[n];
A000265(n) = (n/2^valuation(n, 2));
A001511(n) = 1+valuation(n, 2);
A302045(n) = A001511(A078898(n));
A302044(n) = { my(c = A000265(A078898(n))); if(1==c, 1, my(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)); };
A302052(n) = if(n<=1, 1, if((A302045(n)%2), 0, A302052(A302044(n))));
(PARI)
\\ Or, using also some of the code from above:
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A055396(n) = if(1==n, 0, primepi(A020639(n)));
A250246(n) = if(1==n, n, my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));
A302052(n) = if(!n, 1, issquare(A250246(n)));

Crossrefs

Cf. A010052, A250246, A302044, A302045, A302053 (positions of ones).

Cf. also A253557, A302041, A302050, A302051, A302039, A302055 for other similar analogs.

Sequence in context: A014305 A023533 A010052 * A039985 A324822 A127239

Adjacent sequences: A302049 A302050 A302051 * A302053 A302054 A302055

Keyword

nonn

Author

Antti Karttunen, Mar 31 2018

Status

approved