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

1,1

Comments

Subsequence of A120944.

Links

Donovan Johnson, Table of n, a(n) for n = 1..100

Example

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.

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);

Crossrefs

Cf. A000005, A228299-A228301.

Sequence in context: A037044 A251847 A225718 * A116147 A233630 A254696

Adjacent sequences: A228299 A228300 A228301 * A228303 A228304 A228305

Keyword

nonn

Author

Paolo P. Lava, Aug 20 2013

Extensions

More terms from Michel Marcus, Sep 21 2013

First term deleted by Paolo P. Lava, Sep 23 2013

Status

approved