cp's OEIS Frontend

A175729 Numbers n such that the sum of the prime factors with multiplicity of n divides n-1.

%I A175729 #22 Sep 30 2022 10:48:56
%S A175729 6,21,45,52,225,301,344,441,697,1225,1333,1540,1625,1680,1695,1909,
%T A175729 2025,2041,2145,2295,2466,2601,2926,3051,3104,3146,3400,3510,3738,
%U A175729 3888,3901,4030,4186,4251,4375,4641,4675,4693,4930,5005,5085,5244,5425,6025,6105
%N A175729 Numbers n such that the sum of the prime factors with multiplicity of n divides n-1.
%H A175729 Robert Israel, <a href="/A175729/b175729.txt">Table of n, a(n) for n = 1..10000</a>
%F A175729 {n : A001414(n) | (n-1)}. [_R. J. Mathar_, Aug 24 2010]
%e A175729 For example, 21=7x3, 7+3=10 which divides 21-1=20.
%p A175729 A001414 := proc(n) ifactors(n)[2] ; add( op(1,p)*op(2,p),p=%) ; end proc:
%p A175729 isA175729 := proc(n) if (n-1) mod A001414(n) = 0 then true; else false; end if; end proc:
%p A175729 for n from 2 to 10000 do if isA175729(n) then printf("%d,",n) ; end if; end do:
%p A175729 # _R. J. Mathar_, Aug 24 2010
%t A175729 fQ[n_] := Mod[n - 1, Plus @@ Flatten[ Table[ #1, {#2}] & @@@ FactorInteger@ n]] == 0; Select[ Range@ 6174, fQ] (* _Robert G. Wilson v_, Aug 25 2010 *)
%o A175729 (Magma) [k:k in [2..6200]| IsIntegral((k-1)/( &+[m[1]*m[2]: m in Factorization(k)]))]; // _Marius A. Burtea_, Sep 16 2019
%o A175729 (Python)
%o A175729 from sympy import factorint
%o A175729 def ok(n): return n>1 and (n-1)%sum(p*e for p, e in factorint(n).items())==0
%o A175729 print([k for k in range(10**4) if ok(k)]) # _Michael S. Branicky_, Sep 30 2022
%Y A175729 Disjoint from A130871 and A046346.
%Y A175729 Cf. A001414.
%Y A175729 Contains A164643.
%K A175729 easy,nonn
%O A175729 1,1
%A A175729 K. T. Lee (7x3(AT)21cn.com), Aug 23 2010
%E A175729 Extended by _R. J. Mathar_ and _Robert G. Wilson v_, Aug 24 2010