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A334104 Numbers m for which A329697(m) = 4. 9
43, 47, 49, 57, 59, 63, 67, 69, 71, 77, 79, 81, 86, 87, 91, 93, 94, 95, 98, 99, 105, 107, 109, 111, 114, 115, 117, 118, 121, 126, 131, 134, 135, 138, 142, 143, 145, 149, 151, 154, 155, 157, 158, 159, 162, 165, 167, 169, 172, 174, 175, 179, 181, 182, 183, 185, 186, 188, 190, 195, 196, 198, 210, 214, 218, 219, 222, 225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Squares of A334102 form a subsequence.

Among the first 12193 terms (terms < 2^31), there are terms with binary weights 2 - 16, except no terms with weight 13, 14 or 15. For example, 1025 is the first term with binary weight 2, and 65535 is the first term with binary weight 16.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12193; all terms <= 2^31

EXAMPLE

63 = 7*9 is a term as both 7 and 9 are terms of A334102.

65535 = 3*5*17*257 is a term as it is a product of four Fermat primes, thus in four steps all odd primes can be eliminated with p -> (p-1) map.

MATHEMATICA

Position[Array[Length@NestWhileList[# - #/FactorInteger[#][[-1, 1]] &, #, # != 2^IntegerExponent[#, 2] &] - 1 &, 225], 4][[All, 1]] (* Michael De Vlieger, Apr 30 2020 *)

PROG

(PARI)

A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));

isA334104(n) = (4==A329697(n));

CROSSREFS

Row 4 of A334100.

Cf. A052126, A171462, A209229, A329697, A334101, A334102, A334103, A334105, A334106.

Cf. A334094 (primes present).

Sequence in context: A045144 A187777 A105375 * A095503 A095495 A095487

Adjacent sequences:  A334101 A334102 A334103 * A334105 A334106 A334107

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 14 2020

STATUS

approved

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Last modified August 11 12:12 EDT 2022. Contains 356065 sequences. (Running on oeis4.)