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A331741
Squares s such that A331733(s) = sigma(A225546(n)) is congruent to 2 modulo 4.
2
16, 144, 400, 784, 1936, 2704, 3600, 4624, 5776, 7056, 8464, 10000, 13456, 15376, 17424, 19600, 21904, 24336, 26896, 29584, 35344, 38416, 41616, 44944, 48400, 51984, 55696, 59536, 67600, 71824, 76176, 80656, 85264, 90000, 94864, 99856, 104976, 110224, 115600, 121104, 126736, 132496, 138384, 144400, 150544, 163216, 169744, 176400
OFFSET
1,1
COMMENTS
Squares s for which A331733(s) is two times an odd number, i.e., squares s such that A007814(A331733(s)) == 1.
For each term k present, A006519(k) = 2^(2^e)), with A000040(1+e) == 1 (mod 4). See A191218, A228058.
Equal to the sequence A225546(A191218(n)), for n >= 1, when its elements are sorted into ascending order.
FORMULA
{n: A010052(n)*A007814(A331733(n)) == 1}.
MATHEMATICA
Select[Range[100]^2, Mod[DivisorSigma[1, If[# == 1, 1, Apply[Times, Flatten@ Map[Function[{p, e}, Map[Prime[Log2@# + 1]^(2^(PrimePi@ p - 1)) &, DeleteCases[NumberExpand[e, 2], 0]]] @@ # &, FactorInteger[#]]]]], 4] == 2 &] (* Michael De Vlieger, Feb 08 2020 *)
PROG
(PARI)
k=0; for(n=1, 500, if(!(n%2)&&(1==A007814(A331733(n^2))), k++; write("b331741.txt", k, " ", n^2); print(n^2, " -> ", factor(n^2), ", ")));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 03 2020
STATUS
approved