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 A348076 Number k such that k and k+1 both have an equal number of even and odd exponents in their prime factorization (A187039). 5
 44, 75, 98, 116, 147, 171, 175, 207, 244, 332, 368, 387, 404, 507, 548, 603, 604, 656, 724, 800, 832, 844, 847, 891, 908, 931, 963, 1052, 1075, 1083, 1124, 1250, 1251, 1323, 1324, 1412, 1467, 1556, 1587, 1675, 1772, 1791, 2096, 2224, 2312, 2348, 2367, 2511, 2523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS First differs from A049103 and A074172 at n=7. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 44 is a term since 44 = 2^2 * 11 and 44 + 1 = 45 = 3^2 * 5 both have one even and one odd exponent in their prime factorization. MATHEMATICA q[n_] := n == 1 || Count[(e = FactorInteger[n][[;; , 2]]), _?OddQ] == Count[e, _?EvenQ]; Select[Range[2500], q[#] && q[# + 1] &] PROG (Python) from sympy import factorint def aupto(limit): alst, cond = [], False for nxtk in range(3, limit+2): evenodd = [0, 0] for e in factorint(nxtk).values(): evenodd[e%2] += 1 nxtcond = (evenodd[0] == evenodd[1]) if cond and nxtcond: alst.append(nxtk-1) cond = nxtcond return alst print(aupto(2523)) # Michael S. Branicky, Sep 27 2021 CROSSREFS Subsequence of A187039. A074172 is a subsequence. Cf. A049103. Sequence in context: A156812 A171665 A348098 * A348345 A049103 A074172 Adjacent sequences: A348073 A348074 A348075 * A348077 A348078 A348079 KEYWORD nonn AUTHOR Amiram Eldar, Sep 27 2021 STATUS approved

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Last modified February 22 09:46 EST 2024. Contains 370250 sequences. (Running on oeis4.)