A339005 Numbers of the form prime(x) * prime(y) where x properly divides y. Squarefree semiprimes with divisible prime indices.

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

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: A350586 A068198 A064899 * A271550 A315224 A315225

Adjacent sequences: A339002 A339003 A339004 * A339006 A339007 A339008

Keyword

nonn

Author

Gus Wiseman, Dec 05 2020

Status

approved