A128671 Least number k > 0 such that k^p does not divide the denominator of generalized harmonic number H(k,p) nor the denominator of alternating generalized harmonic number H'(k,p), where p = prime(n).

20, 94556602, 444, 104, 77, 3504, 1107, 104, 2948, 903, 77, 1752, 77, 104, 370

Offset: 1

Author

Alexander Adamchuk, Mar 24 2007, Mar 26 2007

Keywords

• nonn
• hard
• more

Comments

Generalized harmonic numbers are defined as H(m,k) = Sum_{i=1..m} 1/i^k. Alternating generalized harmonic numbers are defined as H'(m,k) = Sum_{i=1..m} (-1)^(i+1)*1/i^k.

a(18)..a(24) = {77,104,77,136,104,370,136}. a(26)..a(27) = {77,104}.

a(n) is currently unknown for n = {16,17,25,...}. See more details in Comments at A128672 and A125581.

Examples

			a(2) = A128673(1) = 94556602.
		

Links

• Eric Weisstein's World of Mathematics, Harmonic Number

Crossrefs

Cf. A128670, A001008, A002805, A058313, A058312, A007406, A007407, A119682, A007410, A120296, A125581, A126196, A126197, A128672, A128673, A128674, A128675, A128676.

Formula

a(n) = A128670(prime(n)).

Extensions

a(9) = 2948 and a(12) = 1752 from Max Alekseyev

Edited by Max Alekseyev, Feb 20 2019