A309639 Index of the least harmonic number H_i whose denominator (A002805) is divisible by n.
1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 4, 13, 7, 5, 16, 17, 9, 19, 5, 9, 11, 23, 9, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 7, 9, 37, 19, 13, 8, 41, 9, 43, 11, 9, 23, 47, 16, 49, 25, 17, 13, 53, 27, 11, 8, 19, 29, 59, 5, 61, 31, 9, 64, 13, 11, 67, 17, 24, 7, 71, 9, 73, 37, 25
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
- Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Crossrefs
Programs
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Maple
H:= 1: B[1]:= 1: for n from 2 to 200 do H:= H + 1/n; B[n]:= denom(H) od: f:= proc(n) local F, t0, t; t0:= max(seq(t[1]^t[2],t=ifactors(n)[2])); for t from t0 do if B[t] mod n = 0 then return t fi od end proc: f(1):= 1: map(f, [$1..100]); # Robert Israel, Aug 11 2019
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Mathematica
s = 0; k = 1; t[_] := 0; While[k < 101, s = s + 1/k; lst = Select[ Range@ 100, Mod[Denominator@ s, #] == 0 &]; If[t[#] == 0, t[#] = k] & /@ lst; k++]; t@# & /@ Range@75
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PARI
f(n) = denominator(sum(k=2, n, 1/k)); \\ A002805 a(n) = my(k=1); while(f(k) % n, k++); k; \\ Michel Marcus, Aug 11 2019
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PARI
A309639list(up_to) = { my(s=0,v002805=vector(up_to),v309639=vector(up_to)); v002805[1] = 1; for(k=2,up_to,s += 1/k; v002805[k] = denominator(s)); for(n=1,up_to,for(j=1,up_to,if(!(v002805[j]%n),v309639[n] = j; break))); (v309639); }; \\ Antti Karttunen, Dec 29 2019
Formula
a(n) = n iff n is a power of a prime (A000961).
a(n) < n iff n is a member of A024619.
a(n) >= A034699(n). - Robert Israel, Aug 11 2019
gcd(a(n), n) = A330691(n). - Antti Karttunen, Dec 29 2019
Comments