A228299 Composite squarefree numbers n such that p+d(n) divides n+d(n), where p are the prime factors of n and d(n) the number of divisors of n.

21098, 134930, 343027, 361730, 387127, 751394, 793595, 1344517, 1430449, 1579394, 1794854, 3542797, 5022254, 7930117, 9241627, 12122947, 21089129, 21928717, 49825117, 70233329, 78795074, 90079589, 95208734, 110995807, 124648303, 124964219, 144871634

Offset

1,1

Comments

Subsequence of A120944.

Links

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

Example

Prime factors of 21098 are 2, 7, 11 and 137 while d(21098) = 16. We have that 21098 + 16 = 21114 and 21114 / (2 + 16) =  1173, 21114 / (7 + 16) = 918, 21114 / (11 + 16) = 782 and 21114 / (137 + 16) = 138.

Maple

with (numtheory); P:=proc(q) local a, i, ok, n;
for n from 1 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+tau(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(10^6);

Crossrefs

Cf. A000005, A228300-A228302.

Sequence in context: A316482 A340897 A371354 * A178279 A097239 A346902

Adjacent sequences: A228296 A228297 A228298 * A228300 A228301 A228302

Keyword

nonn

Author

Paolo P. Lava, Aug 20 2013

Extensions

More terms from Michel Marcus, Sep 21 2013

Deleted first term from Paolo P. Lava, Sep 23 2013

Status

approved