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A229324
Composite squarefree numbers n such that p + tau(n) divides n - phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).
8
115, 205, 295, 565, 655, 745, 835, 1195, 1285, 1465, 1555, 1735, 1915, 2005, 2095, 2455, 2545, 2815, 2995, 3085, 3265, 3715, 3805, 3985, 4435, 4705, 4885, 5065, 5155, 5245, 5515, 5965, 6145, 6415, 6505, 6595, 6865, 7045, 7135, 7405, 7495, 7765, 7855, 8035
OFFSET
1,1
COMMENTS
All terms are apparently multiple of 5.
It appears that a(n) = 5*A061240(n+1). - Michel Marcus, Sep 21 2013
LINKS
EXAMPLE
Prime factors of 2815 are 5, 563 and tau(2815) = 4, phi(2815) = 2248. 2815 - 2248 = 567 and 567 / (5 + 4) = 63, 567 / (563 + 4) = 1.
MAPLE
with (numtheory); P:=proc(q) global a, b, c, i, ok, p, n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 then ok:=0; break;
else if not type((n-phi(n))/(a[i][1]+tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(6*10^9);
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Sep 20 2013
EXTENSIONS
Deleted first term, changed b-file and comment by Paolo P. Lava, Sep 23 2013
STATUS
approved