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A326227 Indices of nonsquarefree numerators (A001008) of harmonic numbers H(n) = Sum_{k=1..n} 1/k. 0

%I #27 Jul 04 2019 15:27:46

%S 4,6,7,10,12,16,18,22,28,29,30,36,40,42,46,52,58,60,66,70,72,78,82,88,

%T 96,100,102,106,108,112,126,130,136,138,148,150,156,162,166,172,178,

%U 180,190,192,196,198,210,222,226,228,232,238,240,250,256,262,268,270,276

%N Indices of nonsquarefree numerators (A001008) of harmonic numbers H(n) = Sum_{k=1..n} 1/k.

%C It appears that the first term of A001008 having a cubic factor is A001008(848) = 11^3 * 1871 * C359.

%C By Wolstenholme's Theorem, p^2 divides A001008(p-1) whenever p >= 5 is prime (cf. A076637); see A308968 for illustration. Therefore, A006093 \ {1, 2} (primes - 1) is a subsequence. (Thanks to _Bernard Schott_.)

%o (PARI) is_A326227(n)={n>3&&vecmax(factor(A001008(n))[,2])>1} \\ Add ,0 in factor() for much faster but possibly incorrect results [false negative].

%o for(n=1,oo, is_A326227(n) && print1(n","))

%Y Cf. A001008, A076637, A322434.

%Y Cf. A308967 (number of prime factors), A308968 (table of factorization), A308969 (table of prime divisors), A308970 & A308971 (smallest & largest prime factor) of A001008(n).

%K nonn,more,hard

%O 1,1

%A _M. F. Hasler_, Jul 03 2019

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