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

4, 6, 7, 10, 12, 16, 18, 22, 28, 29, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 96, 100, 102, 106, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238, 240, 250, 256, 262, 268, 270, 276

Offset: 1

Author

M. F. Hasler, Jul 03 2019

Keywords

• nonn
• more
• hard

Comments

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

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.)

Crossrefs

Cf. A001008, A076637, A322434.

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

Programs

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].
for(n=1,oo, is_A326227(n) && print1(n","))