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0, 0, 1, 1, 1, 0, 3, 2, 2, 3, 3, 2, 2, 3, 1, 3, 6, 3, 5, 1, 4, 5, 7, 2, 3, 4, 3, 0, 8, 4, 10, 4, 4, 7, 2, 4, 4, 7, 3, 4, 10, 4, 9, 4, 3, 9, 13, 4, 4, 4, 7, 7, 15, 4, 5, 5, 6, 9, 15, 4, 7, 10, 3, 5, 4, 6, 12, 6, 8, 5, 19, 5, 9, 6, 4, 8, 3, 5, 19, 4, 3, 11, 20, 4, 7, 11, 9, 6, 22, 4, 4, 8, 11, 15, 7, 5, 24, 5, 3, 5, 20
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OFFSET
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1,7
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COMMENTS
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a(n) tells about the degree of relatedness between n and sigma(n) in Doudna tree (see the illustration in A005940). It is 0 for those n where sigma(n) is one of the descendants of n, 1 for those n where the nearest common ancestor of n and sigma(n) is the parent of n, 2 for those n where the nearest common ancestor of n and sigma(n) is the grandparent of n, and so on.
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LINKS
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FORMULA
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PROG
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(PARI)
Abincompreflen(x, y) = if(!x || !y, 0, my(xl=A000523(x), yl=A000523(y), s=min(xl, yl), k=0); x >>= (xl-s); y >>= (yl-s); while(s>=0 && !bitand(1, bitxor(x>>s, y>>s)), s--; k++); (k));
A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A061395(n) = if(n>1, primepi(vecmax(factor(n)[, 1])), 0);
(PARI)
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A347381(n) = if(1==n, 0, my(lista=List([]), i, k=n, stemvec, stemlen, sbr=sigma(n)); while(k>1, listput(lista, k); k = A252463(k)); stemvec = Vecrev(Vec(lista)); stemlen = #stemvec; while(1, if((i=vecsearch(stemvec, sbr))>0, return(stemlen-i)); sbr = A252463(sbr)));
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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