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A319152 Nonprime Heinz numbers of superperiodic integer partitions. 3
9, 25, 27, 49, 81, 121, 125, 169, 243, 289, 343, 361, 441, 529, 625, 729, 841, 961, 1331, 1369, 1521, 1681, 1849, 2187, 2197, 2209, 2401, 2809, 3125, 3249, 3481, 3721, 4225, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7569, 7921, 8281, 9261, 9409, 10201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A subsequence of A001597.

A number n is in the sequence iff n = 2 or the prime indices of n have a common divisor > 1 and the Heinz number of the multiset of prime multiplicities of n, namely A181819(n), is already in the sequence.

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

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

The sequence of partitions whose Heinz numbers belong to the sequence begins: (22), (33), (222), (44), (2222), (55), (333), (66), (22222), (77), (444), (88), (4422), (99), (3333), (222222).

MATHEMATICA

supperQ[n_]:=Or[n==2, And[GCD@@PrimePi/@FactorInteger[n][[All, 1]]>1, supperQ[Times@@Prime/@FactorInteger[n][[All, 2]]]]];

Select[Range[10000], And[!PrimeQ[#], supperQ[#]]&]

CROSSREFS

Cf. A001597, A056239, A072774, A181819, A182850, A289509, A296150, A298748, A304464, A305732, A317246, A317257, A319149, A319151.

Sequence in context: A062739 A075109 A319165 * A244623 A117580 A280609

Adjacent sequences:  A319149 A319150 A319151 * A319153 A319154 A319155

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 12 2018

STATUS

approved

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Last modified November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)