A368950 - OEIS

A368950

Numbers with 11 odd divisors.

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

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OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

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.

MAPLE

N:= 10^10: # for terms <= N

R:= NULL: p:= 2:

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

MATHEMATICA

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]]]]