A124432
Denominator of Sum_{k=1..n} 1/H(k), where H(k) = Sum_{j=1..k} 1/j is the k-th harmonic number.
Original entry on oeis.org
1, 1, 3, 33, 825, 113025, 5538225, 60920475, 46360481475, 330503872435275, 20160736218551775, 1687675389591187637025, 145175524688023551724527525, 166370135063802174111446471957325, 194941377468714112878127508925972294225
Offset: 0
-
f[n_] := Denominator[ Sum[ 1/HarmonicNumber[j], {j, n}]]; Table[ f[n], {n, 0, 14}] (* Ray Chandler, Dec 16 2006 *)
-
a(n) = denominator(sum(k=1, n, 1/sum(j=1, k, 1/j))); \\ Michel Marcus, Mar 24 2023
A229556
Array read by antidiagonals. Rows are the numerators of consecutive harmonic transforms starting with a first row 1, 1, 1, ....
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 11, 5, 1, 1, 5, 25, 73, 8, 1, 1, 6, 137, 2221, 749, 13, 1, 1, 7, 49, 353777, 1964654, 12657, 21, 1, 1, 8, 363, 19595573, 786674809783, 14862065179, 343693, 34, 1, 1, 9, 761, 239046803, 17003676861538314284, 13379715149864207035877, 35955580499839
Offset: 1
Table begins
1, 1, 1, 1, ...
1, 2, 3, 4, ...
1, 3, 11, 25, ...
1, 5, 73, 2221, ...
1, 8, 749, 1964654, ...
which are the numerators of
1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, ...
1, 3/2, 11/6, 25/12, 137/60, ...
1, 5/3, 73/33, 2221/825, 353777/113025, ...
1, 8/5, 749/365, 1964654/810665, 786674809783/286794631705, ...
-
A229556A := proc(n,k)
option remember;
if n = 1 then
1;
else
add( 1/procname(n-1,c),c=1..k) ;
end if;
end proc:
A229556 := proc(n,k)
numer(A229556A(n,k)) ;
end proc:
for d from 2 to 12 do
for k from d-1 to 1 by -1 do
printf("%d,",A229556(d-k,k)) ;
end do:
end do:
A234714
Numerator of sum_{k=1..n} 1/(k*H(k)) where H(k) is the harmonic number H(k) = sum_{j=1..n} 1/j.
Original entry on oeis.org
0, 1, 4, 50, 1349, 194713, 9917687, 112451057, 87707471002, 638247495586258, 39621419345255038, 3367553690081394959018, 293578866124447319211215128, 340463591070905769538621961175104, 403214792232827898020426758621769680732, 16787247654077861265551571547714793328259156
Offset: 0
-
nmax = 54; Table[ Numerator[ Sum[ 1/(k HarmonicNumber[k]), {k, 1, n} ] ], {n, 0, nmax} ]
A234715
Denominator of sum_{k=1..n} 1/(k*H(k)) where H(k) is the harmonic number H(k) = sum_{j=1..n} 1/j.
Original entry on oeis.org
1, 1, 3, 33, 825, 113025, 5538225, 60920475, 46360481475, 330503872435275, 20160736218551775, 1687675389591187637025, 145175524688023551724527525, 166370135063802174111446471957325, 194941377468714112878127508925972294225, 8038017817167489016303831575544615607779425
Offset: 0
-
nmax = 54; Table[ Denominator[ Sum[ 1/(k HarmonicNumber[k]), {k, 1, n} ] ], {n, 0, nmax} ]
A095992
a(1) = 30; for n > 1, a(n+1) = a(n) + {product of nonzero digits of a(n)}.
Original entry on oeis.org
30, 33, 42, 50, 55, 80, 88, 152, 162, 174, 202, 206, 218, 234, 258, 338, 410, 414, 430, 442, 474, 586, 826, 922, 958, 1318, 1342, 1366, 1474, 1586, 1826, 1922, 1958, 2318, 2366, 2582, 2742, 2854, 3174, 3258, 3498, 4362, 4506, 4626, 4914, 5058, 5258, 5658
Offset: 1
Julien Piquet (julipiquet(AT)yahoo.fr), Jul 18 2004
- From a puzzle; explanation found by Pierre Roger.
Cf.
A063108,
A096347,
A096972,
A063108,
A063425,
A096922,
A096923,
A096924,
A096925,
A096926,
A096927,
A096928,
A096929,
A096930,
A096931,
A096973,
A096987.
-
a[1] = 30; a[n_] := a[n] = Block[{s = Sort[ IntegerDigits[a[n - 1]]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; a[n - 1] + Times @@ s]; Table[ a[n], {n, 50}]
nxt[n_] := n+Times@@Select[IntegerDigits[n], #>0&]; NestList[nxt,30,50] (* Harvey P. Dale, Jan 08 2011 *)
The proposer suggests that this web site may contain other sequences also.
Showing 1-5 of 5 results.
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