A226774 Integers a(n) = Sum_{i=1..q} 1/d(i) where d(i) are the divisors of A225110(n) for some q.

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,2

Comments

The corresponding q are 1, 4, 4, 6, 4, 4, 4, 4, 4, 4, 16, 4, 4, 4, 4, 15, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 24, 4, 4, 4, 4, 4, 4, ...

By convention, a(1)=1. For a majority of n, a(n) = 2.

a(n) = 3 for n = 11, 16, 52, 145, 634, ... where A225110(n) = 120, 180, 672, 1890, 8460, ...

a(n) = 4 for n = 2284, 2476, 6871, ... where A225110(n) = 30240, 32760, 90720, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Example

a(16) = 3 because the divisors of A225110(16) = 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 and 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/9 + 1/10 + 1/12 + 1/15 + 1/18 + 1/20 + 1/30 + 1/36 + 1/45 = 3.

Maple

with(numtheory): for n from 1 to 2000 do:x:=divisors(n):n1:=nops(x):s:=0:ii:=0:for q from 1 to
n1 while(ii=0) do:s:=s+1/x[q]:if s=floor(s) and q>1 then ii:=1: printf(`%d, `, s):else fi:od:od:

Prog

(PARI)
either_A226774_or_0(n) = { if(1==n, return(1)); my(divs=divisors(n), s=0); for(i=1, #divs, s += (1/divs[i]); if((1==denominator(s))&&(i>1), return(s))); return(0); };
up_to = 16384; i=0; n=0; while(i<up_to, n++; s = either_A226774_or_0(n); if(s, i++; write("b226774.txt", i, " ", s)));
\\ Antti Karttunen, Dec 16 2017

Crossrefs

Cf. A225110.

Sequence in context: A339171 A083311 A104230 * A037968 A303378 A074908

Adjacent sequences: A226771 A226772 A226773 * A226775 A226776 A226777

Keyword

nonn

Author

Michel Lagneau, Jun 17 2013

Status

approved