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

1,2

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

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 *)

Prog

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

Crossrefs

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

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

Sequence in context: A090756 A038351 A068871 * A327346 A030430 A059313

Adjacent sequences: A004612 A004613 A004614 * A004616 A004617 A004618

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved