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0, 0, 1, 1, 1, 0, 2, 2, 3, 3, 1, 2, 3, 3, 3, 3, 3, 3, 4, 1, 2, 4, 3, 2, 4, 4, 4, 4, 4, 4, 3, 4, 2, 5, 4, 0, 5, 4, 3, 4, 3, 5, 3, 4, 4, 4, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 6, 4, 3, 4, 4, 6, 3, 5, 4, 6, 6, 4, 4, 4, 1, 4, 5, 6, 4, 5, 6, 6, 5, 4, 5, 5, 5, 5, 5, 3, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
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OFFSET
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0,7
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COMMENTS
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This sequence tells how near sigma(x) is to each x in Doudna-tree, A005940, with x iterating over the vertices of the tree in the breadth-first fashion. Positions that correspond to perfect numbers or (hypothetical) odd triperfect numbers get values 0 and 1 respectively. 1's occur also elsewhere. (Clarified Jul 03 2023)
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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));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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