cp's OEIS Frontend

A004615 Divisible only by primes congruent to 1 mod 5.

%I A004615 #49 Oct 26 2023 00:41:12
%S A004615 1,11,31,41,61,71,101,121,131,151,181,191,211,241,251,271,281,311,331,
%T A004615 341,401,421,431,451,461,491,521,541,571,601,631,641,661,671,691,701,
%U A004615 751,761,781,811,821,881,911,941
%N A004615 Divisible only by primes congruent to 1 mod 5.
%C A004615 Also numbers with all divisors ending with digit 1.
%C A004615 Union of number 1, A030430 and A068872. - _Jaroslav Krizek_, Feb 12 2012
%C A004615 Also numbers with all divisors ending with the same digit; as 1 divides all the integers, this digit is necessarily 1 (see first comment); hence, for these numbers m: A330348(m) = A000005(m). - _Bernard Schott_, Nov 09 2020
%H A004615 Reinhard Zumkeller, <a href="/A004615/b004615.txt">Table of n, a(n) for n = 1..10000</a>
%t A004615 ok[1]=True;ok[n_]:=And@@(Mod[#,5]==1&)/@FactorInteger[n][[All,1]];Select[Range[2000],ok] (* _Vincenzo Librandi_, Aug 21 2012 *)
%t A004615 Select[Range[1000],Union[Mod[#,5]&/@FactorInteger[#][[All,1]]]=={1}&] (* _Harvey P. Dale_, Apr 19 2019 *)
%o A004615 (Haskell)
%o A004615 a004615 n = a004615_list !! (n-1)
%o A004615 a004615_list = filter (all (== 1) . (map (`mod` 5) . a027748_row)) [1..]
%o A004615 -- _Reinhard Zumkeller_, Apr 16 2012
%o A004615 (Magma) [n: n in [1..1500] | forall{d: d in PrimeDivisors(n) | d mod 5 eq 1}]; // _Vincenzo Librandi_, Aug 21 2012
%o A004615 (PARI) is(n)=#select(p->p%5!=1, factor(n)[,1])==0 \\ _Charles R Greathouse IV_, Mar 11 2014
%Y A004615 Cf. A027748, A030430 (primes), A068872 (composites).
%Y A004615 Cf. A010879, A027750, A002808, A330348, A338784 (subsequence).
%K A004615 nonn
%O A004615 1,2
%A A004615 _N. J. A. Sloane_
%E A004615 A206291 merged in by _Franklin T. Adams-Watters_, Sep 21 2012