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 A302052 Characteristic function for A302053; an analog of A010052 (char. fun of squares) for the nonstandard factorization based on the sieve of Eratosthenes (A083221). 10
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 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

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Last modified April 8 12:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)