A318991 Numbers whose consecutive prime indices are divisible. Heinz numbers of integer partitions in which each part is divisible by the next.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 71, 72, 73, 74, 76, 78, 79, 80

Offset: 1

Author

Gus Wiseman, Sep 06 2018

Keywords

• nonn

Comments

A prime index of n is a number m such that prime(m) divides n.

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Examples

			The sequence of all dividing partitions (columns) begins:
   1  2  1  3  2  4  1  2  3  5  2  6  4  1  7  2  8  3  4  5  9  2  3  6  2  4
         1     1     1  2  1     1     1  1     2     1  2  1     1  3  1  2  1
                     1           1        1     1     1           1        2  1
                                          1                       1
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001221, A001222, A003238, A008480, A300912, A318990, A318992, A318993.

Programs

Mathematica

Select[Range[100],Or[#==1,PrimePowerQ[#],Divisible@@Reverse[PrimePi/@FactorInteger[#][[All,1]]]]&]

PARI

ok(n)={my(v=apply(primepi, factor(n)[,1])); for(i=2, #v, if(v[i]%v[i-1], return(0))); 1} \\ Andrew Howroyd, Oct 26 2018