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 A297167 a(1) = 0, for n > 1, a(n) = -1 + the excess of n (A046660) + the index of the largest prime factor (A061395). 25
 0, 0, 1, 1, 2, 1, 3, 2, 2, 2, 4, 2, 5, 3, 2, 3, 6, 2, 7, 3, 3, 4, 8, 3, 3, 5, 3, 4, 9, 2, 10, 4, 4, 6, 3, 3, 11, 7, 5, 4, 12, 3, 13, 5, 3, 8, 14, 4, 4, 3, 6, 6, 15, 3, 4, 5, 7, 9, 16, 3, 17, 10, 4, 5, 5, 4, 18, 7, 8, 3, 19, 4, 20, 11, 3, 8, 4, 5, 21, 5, 4, 12, 22, 4, 6, 13, 9, 6, 23, 3, 5, 9, 10, 14, 7, 5, 24, 4, 5, 4, 25, 6, 26, 7, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A252464(n) - A001221(n). For n > 1, a(n) = A033265(A156552(n)) = A297113(n) - 1. For n > 1, a(n) = A046660(n) + A061395(n) - 1. - Antti Karttunen, Mar 13 2018 MATHEMATICA Array[-1 + PrimeOmega@ # - PrimeNu@ # + PrimePi[FactorInteger[#][[-1, 1]]] /. k_ /; k < 0 -> 0 &, 105] (* or, slightly faster *) Array[-1 + Length@ # - Length@ Union@ # + PrimePi@ Last@ # /. k_ /; k < 0 -> 0 &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, #] &@ FactorInteger[#] &, 105] (* Michael De Vlieger, Mar 13 2018 *) PROG (PARI) A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530. A252464(n) = if(1==n, 0, (bigomega(n) + A061395(n) - 1)); A297167(n) = (A252464(n) - omega(n)); \\ Or just as: A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1)); \\ Antti Karttunen, Mar 13 2018 (Scheme) (define (A297167 n) (- (A252464 n) (A001221 n))) CROSSREFS Cf. A001221, A033265, A046660, A061395, A156552, A252464, A297113, A297168, A300827. Sequence in context: A103151 A035221 A035191 * A325224 A303389 A276166 Adjacent sequences:  A297164 A297165 A297166 * A297168 A297169 A297170 KEYWORD nonn AUTHOR Antti Karttunen, Feb 27 2018 EXTENSIONS Name changed, original equivalent definition is the first entry in the Formula section - Antti Karttunen, Mar 13 2018 STATUS approved

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Last modified November 23 16:18 EST 2020. Contains 338590 sequences. (Running on oeis4.)