A267983 -id:A267983 - cp's OEIS frontend

59049, 118098, 236196, 472392, 944784, 1889568, 3779136, 7558272, 9765625, 15116544, 19531250, 30233088, 39062500, 60466176, 78125000, 120932352, 156250000, 241864704, 282475249, 312500000, 483729408, 564950498, 625000000, 967458816, 1129900996, 1250000000, 1934917632

Offset: 1

Hartmut F. W. Hoft, Jan 10 2024

nonn

Every number in this sequence has the form 2^k * p^10, k >= 0, where p is an odd prime. Exactly 11 different width patterns (A341969) of the symmetric representation of sigma are instantiated by the numbers in this sequence. The width pattern becomes unimodal for k >= floor(log_2(p^10)), see A367370 and A367377.

			a(1) = 59049 = 3^10, a(9) = 5^10 = 9765625 is the smallest number with prime factor 5, a(19) = 282475249 is the smallest number with prime factor 7 and a(27) = 2^floor(log_2(3^10)) * 3^10 = 32768 * 59049 = 1934917632 is the smallest whose width pattern of its symmetric representation of sigma is unimodal.

Cf. A267983 (lists the sequences of numbers with 1 .. 10 odd divisors), A367370, A367377.

Cf. A235791, A237048, A237270, A237593, A241008, A241010, A249223, A341969.

N:= 10^10: # for terms <= N
R:= NULL: p:= 2:
do
  p:= nextprime(p);
  if p^10 > N then break fi;
  R:= R, seq(2^i*p^10, i = 0 .. floor(log[2](N/p^10)))
od:
sort([R]); # Robert Israel, Jan 16 2024

numL[p_, b_] := Map[2^# p^10&, Range[0, Floor[Log[2, b/p^10]]]]
primeL[b_] := Most[NestWhileList[NextPrime[#]&, 3, #^10<=b&]]
a368950[b_] := Union[Flatten[Map[numL[#, b]&, primeL[b]]]]
a368950[2 10^9]

cp's OEIS Frontend

A368950 Numbers with 11 odd divisors.

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