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A318991
Numbers whose consecutive prime indices are divisible. Heinz numbers of integer partitions in which each part is divisible by the next.
52
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 06 2018
STATUS
approved