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A072984 Least k such that prime(n) appears in the factorization of A001008(k) (the numerator of the k-th harmonic number). 9
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 (list; graph; refs; listen; history; text; internal format)
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: A002849 A329492 A163234 * A317310 A231655 A018841

Adjacent sequences:  A072981 A072982 A072983 * A072985 A072986 A072987

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 21 2002

STATUS

approved

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Last modified June 4 06:41 EDT 2020. Contains 334822 sequences. (Running on oeis4.)