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 A293460 a(n) = Sum_{k=1..n} sign(omega(n+1) - omega(n)) (where omega(m) = A001221(m), the number of distinct primes dividing m). 1
 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 3, 2, 3, 3, 4, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The sign function is defined by: - sign(0) = 0, - sign(n) = +1 for any n > 0, - sign(n) = -1 for any n < 0. a(n) corresponds to the number of integers up to n in A294277 minus the number of integers up to n in A294278. The first negative value occurs at a(178) = -1. Will this sequence change sign indefinitely? LINKS Georg Fischer, Table of n, a(n) for n = 0..1000 Rémy Sigrist, Line graph of the first 10000 terms Rémy Sigrist, Line graph of the first 100000000 terms Rémy Sigrist, Line graph of the first 1000000000 terms Rémy Sigrist, Line graph of the first 10000000000 terms FORMULA a(0) = 0, and for any n > 0: - a(A294277(n)) = a(A294277(n)-1) + 1, - a(A006049(n)) = a(A006049(n)-1), - a(A294278(n)) = a(A294278(n)-1) - 1. Also: a(n) = #{ k / A294277(k) <= n } - #{ k / A294278(k) <= n }. EXAMPLE The following table shows the first terms of the sequence, alongside sign(omega(n+1)-omega(n)), omega(n+1) and omega(n): n       a(n)    sign    w(n+1)  w(n) -       ----    ----    ------  ---- 0       0 1       1       1       1       0 2       1       0       1       1 3       1       0       1       1 4       1       0       1       1 5       2       1       2       1 6       1       -1      1       2 7       1       0       1       1 8       1       0       1       1 9       2       1       2       1 10      1       -1      1       2 11      2       1       2       1 12      1       -1      1       2 13      2       1       2       1 14      2       0       2       2 15      1       -1      1       2 16      1       0       1       1 17      2       1       2       1 18      1       -1      1       2 19      2       1       2       1 20      2       0       2       2 PROG (PARI) s = 0; for (n=1, 87, print1 (s ", "); s += sign(omega(n+1)-omega(n))) CROSSREFS Cf. A001221, A006049, A294277, A294278. Sequence in context: A302041 A302031 A237353 * A231813 A158210 A322307 Adjacent sequences:  A293457 A293458 A293459 * A293461 A293462 A293463 KEYWORD sign AUTHOR Rémy Sigrist, Oct 26 2017 STATUS approved

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Last modified September 25 00:48 EDT 2020. Contains 337333 sequences. (Running on oeis4.)