OFFSET
1,1
COMMENTS
1 + sum of the indices of the first two numbers in A003215 that are divisible by n if 1 + the sum of those indices equals n.
From Bernard Schott, Mar 31 2021: (Start)
Positive integers m that can be primitively represented as m = k^2+k*q+q^2 with 1 <= k < q and gcd(k,q)=1 in exactly 1 way. For example: 7 = 1 + 1*2 + 2^2.
Positive integers m such that m^2 can be primitively represented as k^2-k*q+q^2 with 1 <= k < q and gcd(k,q)= 1 in exactly 2 ways. For example: 7^2 = 3^2 - 3*8 + 8^2 = 5^2 - 5*8 + 8^2.
Length of the middle side b of the primitive triangles such that A < B < C with an angle B = 60 degrees and that appears precisely twice consecutively in A335895. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Hex Number.
EXAMPLE
MAPLE
N:= 1000: # for terms <= N
sort(map(p -> seq(p^i, i=1..floor(log[p](N))), select(isprime, [seq(i, i=1..N, 6)]))): # Robert Israel, Dec 02 2019
MATHEMATICA
Select[a=6Range@100+1, PrimePowerQ@#&&MemberQ[a, First@@FactorInteger@#]&] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
PROG
(PARI) a133290(uptolimit)={my(a=vector(uptolimit));
for(n=1, oo, my(j=6*n+1); if(j>#a, break); if(isprime(j), for(k=1, oo, my(m=j^k); if(m>#a, break, a[m]++)))); for(k=1, #a, if(a[k], print1(k, ", ")))};
a133290(601) \\ Hugo Pfoertner, Dec 03 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Mats Granvik, Oct 16 2007, Oct 20 2007
STATUS
approved