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A366243
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Numbers that are products of "Fermi-Dirac primes" (A050376) that are powers of primes with exponents that are not powers of 4.
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10
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1, 4, 9, 25, 36, 49, 100, 121, 169, 196, 225, 256, 289, 361, 441, 484, 529, 676, 841, 900, 961, 1024, 1089, 1156, 1225, 1369, 1444, 1521, 1681, 1764, 1849, 2116, 2209, 2304, 2601, 2809, 3025, 3249, 3364, 3481, 3721, 3844, 4225, 4356, 4489, 4761, 4900, 5041, 5329
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OFFSET
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1,2
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COMMENTS
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Equivalently, numbers that are products of "Fermi-Dirac primes" that are powers of primes with exponents that are powers of 2 with odd exponents.
Products of distinct numbers of the form p^(2^(2*k-1)), where p is prime and k >= 1.
Numbers whose prime factorization has exponents that are positive terms of A062880.
Every integer k has a unique representation as a product of 2 numbers: one is in this sequence and the other is in A366242: k = A366245(k) * A366244(k).
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = Product_{k>=0} zeta(2^(2*k+1))/zeta(2^(2*k+2)) = 1.52599127273749217982... (this is the constant c in A366242).
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MATHEMATICA
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mdQ[n_] := AllTrue[IntegerDigits[n, 4], # < 2 &]; q[e_] := EvenQ[e] && mdQ[e/2]; Select[Range[6000], # == 1 || AllTrue[FactorInteger[#][[;; , 2]], q] &]
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PROG
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(PARI) ismd(n) = {my(d = digits(n, 4)); for(i = 1, #d, if(d[i] > 1, return(0))); 1; }
is(n) = {my(e = factor(n)[ , 2]); for(i = 1, #e, if(e[i]%2 || !ismd(e[i]/2), return(0))); 1; }
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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