A072984 Least k such that prime(n) appears in the factorization of A001008(k) (the numerator of the k-th harmonic number).

2, 4, 6, 3, 12, 16, 18, 22, 13, 30, 17, 40, 13, 46, 22, 58, 10, 66, 70, 72, 78, 82, 88, 11, 100, 102, 106, 25, 112, 126, 130, 5, 138, 148, 150, 156, 162, 166, 71, 178, 180, 190, 192, 196, 38, 210, 222, 22, 228, 232, 238, 240, 250, 66, 262, 33, 58, 276, 280, 282

Offset

2,1

Comments

a(n)<=n for n =2,5,14,18,25,29,33,46,49,...

For p = prime(n), Boyd defines J_p to be the set of numbers k such that p divides A001008(k). This sequence gives the smallest elements of J_p. The largest elements of J_p are given by A177734. The sizes of J_p are given by A092103.

Links

T. D. Noe, Table of n, a(n) for n = 2..1000

David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302. [WARNING: Table 2 contains miscalculations for p=19, 47, 59, ... - Max Alekseyev, Feb 10 2016]

A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.

Mathematica

A072984[n_] := Module[{p, k, sum},
   p = Prime[n]; k = 1; sum = 1/k;
   While[! Divisible[Numerator[sum], p],
    k++; sum += 1/k];
   Return[k]];
Table[A072984[n], {n, 2, 61}] (* Robert Price, May 01 2019 *)

Prog

(PARI) a(n)=if(n<0, 0, s=1; while(numerator(sum(k=1, s, 1/k))%prime(n)>0, s++); s)

Crossrefs

Cf. A092101 (harmonic primes), A092102 (non-harmonic primes), A092103 (size of Jp).

Sequence in context: A163234 A366111 A348022 * A339671 A367198 A317310

Adjacent sequences: A072981 A072982 A072983 * A072985 A072986 A072987

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 21 2002

Status

approved