A228302 Composite squarefree numbers n such that p+d(n) divides n-d(n) for all prime factors p of n, where d(n) is the number of divisors of n.
4958, 51653, 55583, 1251574, 4909102, 5430797, 5785073, 6096931, 13892243, 14058781, 14809517, 16699426, 27391073, 32426566, 32673383, 38669686, 43459682, 44762461, 53638783, 69836866, 74975761, 75226313, 85607461, 96973703, 105139141, 122864065
Offset: 1
Keywords
Examples
Prime factors of 51653 are 7, 47 and 157 while d(51653) = 8. We have that 51653 - 8 = 51645 and 51645 / (7 + 8) = 3443, 51645 / (47 + 8) = 939 and 51645 / (157 + 8) = 313.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..100
Programs
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Maple
with(numtheory); P:=proc(q) local a,i,ok,p,n; for n from 1 to q do if not isprime(n) and issqrfree(n) then a:=ifactors(n)[2]; ok:=1; for i from 1 to nops(a) do if not type((n-tau(n))/(a[i][1]+tau(n)),integer) then ok:=0; break; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^9);
Extensions
More terms from Michel Marcus, Sep 21 2013
First term deleted by Paolo P. Lava, Sep 23 2013
Comments