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A369563
Powerful numbers whose prime factors are all of the form 4*k + 1.
5
1, 25, 125, 169, 289, 625, 841, 1369, 1681, 2197, 2809, 3125, 3721, 4225, 4913, 5329, 7225, 7921, 9409, 10201, 11881, 12769, 15625, 18769, 21025, 21125, 22201, 24389, 24649, 28561, 29929, 32761, 34225, 36125, 37249, 38809, 42025, 48841, 50653, 52441, 54289, 54925
OFFSET
1,2
COMMENTS
Closed under multiplication.
FORMULA
Sum_{n>=1} 1/a(n) = Product_{primes p == 1 (mod 4)} (1 + 1/(p*(p-1))) = A175647 * A334424 = 1.0654356335... .
MATHEMATICA
q[n_] := n == 1 || AllTrue[FactorInteger[n], Mod[First[#], 4] == 1 && Last[#] > 1 &]; Select[Range[50000], q]
PROG
(PARI) is(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 1]%4 != 1 || f[i, 2] == 1, return(0))); 1; }
CROSSREFS
Intersection of A001694 and A004613.
Subsequence: A146945.
Similar sequence: A352492, A369564, A369565, A369566.
Sequence in context: A304422 A280390 A225388 * A146945 A044357 A044738
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 26 2024
STATUS
approved