A331741 Squares s such that A331733(s) = sigma(A225546(n)) is congruent to 2 modulo 4.

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.

Links

Table of n, a(n) for n=1..48.

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), ", ")));

Crossrefs

Cf. A006519, A007814, A010052, A067403, A191218, A225546, A228058, A331733, A331734.

Sequence in context: A358262 A328224 A017114 * A092820 A060300 A128985

Adjacent sequences: A331738 A331739 A331740 * A331742 A331743 A331744

Keyword

nonn

Author

Antti Karttunen, Feb 03 2020

Status

approved