cp's OEIS Frontend

A331082 Smallest number having exactly n divisors ending with 3 or 7.

%I A331082 #15 Mar 21 2021 13:08:13
%S A331082 3,21,63,189,567,693,3969,2079,5733,6237,413343,9009,74529,43659,
%T A331082 51597,27027,1750329,63063,26040609,81081,464373,670761,219667417263,
%U A331082 153153,2528253,819819,693693,729729,160137547184727,567567,6036849,459459,37614213,19253619
%N A331082 Smallest number having exactly n divisors ending with 3 or 7.
%C A331082 A term cannot be a multiple of either 2 or 5 since removing these factors does not alter the number of divisors ending with 3 or 7.
%C A331082 All terms must be in A331029.
%e A331082 a(1) = 3: divisors of 3 are 1, 3*. (* marks divisors ending in 3 or 7.)
%e A331082 a(2) = 21: divisors of 21 are 1, 3*, 7*, 21.
%e A331082 a(3) = 63: divisors of 63 are 1, 3*, 7*, 9, 21, 63*.
%e A331082 a(4) = 189: divisors of 189 are 1, 3*, 7*, 9, 21, 27*, 63*, 189.
%o A331082 (PARI) a(n)={forstep(k=1, oo, 2, if(sumdiv(k, d, abs(d%10-5)==2) == n, return(k)))}
%o A331082 (PARI) \\ faster program: needs lista331029 defined in A331029.
%o A331082 a(n)={my(lim=1); while(1, lim*=10; my(S=lista331029(lim)); for(i=1, #S, my(k=S[i]); if(sumdiv(k, d, abs(d%10-5)==2)==n, return(k))))}
%o A331082 (Python)
%o A331082 from sympy import divisors
%o A331082 def count37(iterable): return sum(i%10 in [3, 7] for i in iterable)
%o A331082 def a(n):
%o A331082   m = 2
%o A331082   while count37(divisors(m)) != n: m += 1
%o A331082   return m
%o A331082 print([a(n) for n in range(1, 17)]) # _Michael S. Branicky_, Mar 21 2021
%Y A331082 Cf. A085645, A331029.
%K A331082 nonn,base
%O A331082 1,1
%A A331082 _Andrew Howroyd_, Jan 08 2020