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A302050 An analog of Möbius function (A008683) for nonstandard factorization based on the sieve of Eratosthenes (A083221). 11
1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 0, 1, -1, 0, 0, 1, 1, 0, -1, -1, -1, 0, 0, 1, 1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1, -1, 0, -1, 1, 1, 0, 1, 0, -1, 0, 0, -1, -1, 0, -1, 1, 1, 0, 1, -1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

LINKS

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

Index entries for sequences generated by sieves

FORMULA

a(1) = 1; for n > 1, if A302045(n) > 1, then a(n) = 0, otherwise a(n) = -1*a(A302044(n)).

a(n) = A008683(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)); };

A302050(n) = if(1==n, n, if(A302045(n)>1, 0, -1*A302050(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)));

A302050(n) = moebius(A250246(n));

CROSSREFS

Cf. A008683, A083221, A250246, A302044, A302045.

Cf. also A253557, A302041, A302051, A302052, A302039, A302055 for other similar analogs.

Sequence in context: A075437 A130047 A293233 * A008683 A008966 A080323

Adjacent sequences:  A302047 A302048 A302049 * A302051 A302052 A302053

KEYWORD

sign

AUTHOR

Antti Karttunen, Apr 01 2018

STATUS

approved

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Last modified June 4 17:14 EDT 2020. Contains 334828 sequences. (Running on oeis4.)