A004615 Divisible only by primes congruent to 1 mod 5.

1, 11, 31, 41, 61, 71, 101, 121, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 341, 401, 421, 431, 451, 461, 491, 521, 541, 571, 601, 631, 641, 661, 671, 691, 701, 751, 761, 781, 811, 821, 881, 911, 941

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also numbers with all divisors ending with digit 1.

Union of number 1, A030430 and A068872. - Jaroslav Krizek, Feb 12 2012

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027748, A030430 (primes), A068872 (composites).

Cf. A010879, A027750, A002808, A330348, A338784 (subsequence).

Programs

Haskell

a004615 n = a004615_list !! (n-1)
a004615_list = filter (all (== 1) . (map (`mod` 5) . a027748_row)) [1..]
-- Reinhard Zumkeller, Apr 16 2012

Magma

[n: n in [1..1500] | forall{d: d in PrimeDivisors(n) | d mod 5 eq 1}]; // Vincenzo Librandi, Aug 21 2012

Mathematica

ok[1]=True;ok[n_]:=And@@(Mod[#,5]==1&)/@FactorInteger[n][[All,1]];Select[Range[2000],ok] (* Vincenzo Librandi, Aug 21 2012 *)
Select[Range[1000],Union[Mod[#,5]&/@FactorInteger[#][[All,1]]]=={1}&] (* Harvey P. Dale, Apr 19 2019 *)

PARI

is(n)=#select(p->p%5!=1, factor(n)[,1])==0 \\ Charles R Greathouse IV, Mar 11 2014

Extensions

A206291 merged in by Franklin T. Adams-Watters, Sep 21 2012