login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339005 Numbers of the form prime(x) * prime(y) where x properly divides y. Squarefree semiprimes with divisible prime indices. 5
6, 10, 14, 21, 22, 26, 34, 38, 39, 46, 57, 58, 62, 65, 74, 82, 86, 87, 94, 106, 111, 115, 118, 122, 129, 133, 134, 142, 146, 158, 159, 166, 178, 183, 185, 194, 202, 206, 213, 214, 218, 226, 235, 237, 254, 259, 262, 267, 274, 278, 298, 302, 303, 305, 314, 319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A squarefree semiprime (A006881) is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

Equals A318990 \ A000290.

EXAMPLE

The sequence of terms together with their prime indices begins:

    6: {1,2}    82: {1,13}  159: {2,16}  259: {4,12}

   10: {1,3}    86: {1,14}  166: {1,23}  262: {1,32}

   14: {1,4}    87: {2,10}  178: {1,24}  267: {2,24}

   21: {2,4}    94: {1,15}  183: {2,18}  274: {1,33}

   22: {1,5}   106: {1,16}  185: {3,12}  278: {1,34}

   26: {1,6}   111: {2,12}  194: {1,25}  298: {1,35}

   34: {1,7}   115: {3,9}   202: {1,26}  302: {1,36}

   38: {1,8}   118: {1,17}  206: {1,27}  303: {2,26}

   39: {2,6}   122: {1,18}  213: {2,20}  305: {3,18}

   46: {1,9}   129: {2,14}  214: {1,28}  314: {1,37}

   57: {2,8}   133: {4,8}   218: {1,29}  319: {5,10}

   58: {1,10}  134: {1,19}  226: {1,30}  321: {2,28}

   62: {1,11}  142: {1,20}  235: {3,15}  326: {1,38}

   65: {3,6}   146: {1,21}  237: {2,22}  334: {1,39}

   74: {1,12}  158: {1,22}  254: {1,31}  339: {2,30}

MATHEMATICA

Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&& Divisible@@Reverse[PrimePi/@First/@FactorInteger[#]]&]

CROSSREFS

A300912 is the version for relative primality.

A318990 is the not necessarily squarefree version.

A339002 is the version for non-relative primality.

A339003 is the version for odd indices.

A339004 is the version for even indices

A001358 lists semiprimes.

A005117 lists squarefree numbers.

A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

A320655 counts factorizations into semiprimes.

A320656 counts factorizations into squarefree semiprimes.

A338898/A338912/A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.

A338899/A270650/A270652 give the prime indices of squarefree semiprimes, with difference A338900.

Cf. A001221, A112798, A166237, A320911, A338901, A338904, A338909.

Sequence in context: A060650 A068198 A064899 * A271550 A315224 A315225

Adjacent sequences:  A339002 A339003 A339004 * A339006 A339007 A339008

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 05 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 14:36 EDT 2021. Contains 345057 sequences. (Running on oeis4.)