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

1,2

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).

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A023808 A331995 A347457 * A322901 A322911 A023756

Adjacent sequences: A318988 A318989 A318990 * A318992 A318993 A318994

Keyword

nonn

Author

Gus Wiseman, Sep 06 2018

Status

approved