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A336620 Numbers that are not a product of elements of A304711. 1
3, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 27, 29, 31, 37, 39, 41, 42, 43, 47, 49, 53, 57, 59, 61, 63, 65, 67, 71, 73, 78, 79, 81, 83, 87, 89, 91, 97, 101, 103, 105, 107, 109, 111, 113, 114, 115, 117, 121, 125, 126, 127, 129, 130, 131, 133, 137, 139, 147, 149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A304711 lists numbers whose distinct prime indices are pairwise coprime.

The first term divisible by 4 is a(421) = 1092.

LINKS

Table of n, a(n) for n=1..60.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

EXAMPLE

The sequence of terms together with their prime indices begins:

      3: {2}         39: {2,6}       78: {1,2,6}

      5: {3}         41: {13}        79: {22}

      7: {4}         42: {1,2,4}     81: {2,2,2,2}

      9: {2,2}       43: {14}        83: {23}

     11: {5}         47: {15}        87: {2,10}

     13: {6}         49: {4,4}       89: {24}

     17: {7}         53: {16}        91: {4,6}

     19: {8}         57: {2,8}       97: {25}

     21: {2,4}       59: {17}       101: {26}

     23: {9}         61: {18}       103: {27}

     25: {3,3}       63: {2,2,4}    105: {2,3,4}

     27: {2,2,2}     65: {3,6}      107: {28}

     29: {10}        67: {19}       109: {29}

     31: {11}        71: {20}       111: {2,12}

     37: {12}        73: {21}       113: {30}

MATHEMATICA

nn=100;

dat=Select[Range[nn], CoprimeQ@@PrimePi/@First/@FactorInteger[#]&];

facsusing[s_, n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsusing[Select[s, Divisible[n/d, #]&], n/d], Min@@#>=d&]], {d, Select[s, Divisible[n, #]&]}]];

Select[Range[nn], facsusing[dat, #]=={}&]

CROSSREFS

A336426 is the version for superprimorials, with complement A181818.

A336497 is the version for superfactorials, with complement A336496.

A336735 is the complement.

A000837 counts relatively prime partitions, with strict case A007360.

A001055 counts factorizations.

A302696 lists numbers with coprime prime indices.

A304711 lists numbers with coprime distinct prime indices.

Cf. A007916, A112798, A302569, A327516, A333228, A335238, A335239, A335240, A335241, A336424, A336568, A336736.

Sequence in context: A244579 A151991 A265166 * A318978 A327755 A322903

Adjacent sequences:  A336617 A336618 A336619 * A336621 A336622 A336623

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 02 2020

STATUS

approved

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Last modified September 27 04:03 EDT 2022. Contains 357052 sequences. (Running on oeis4.)