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A316437 Take the integer partition with Heinz number n, divide all parts by the GCD of the parts, then take the Heinz number of the resulting partition. 4
1, 2, 2, 4, 2, 6, 2, 8, 4, 10, 2, 12, 2, 14, 15, 16, 2, 18, 2, 20, 6, 22, 2, 24, 4, 26, 8, 28, 2, 30, 2, 32, 33, 34, 35, 36, 2, 38, 10, 40, 2, 42, 2, 44, 45, 46, 2, 48, 4, 50, 51, 52, 2, 54, 55, 56, 14, 58, 2, 60, 2, 62, 12, 64, 6, 66, 2, 68, 69, 70, 2, 72, 2, 74, 75, 76, 77, 78, 2, 80, 16, 82, 2, 84, 85, 86, 22, 88, 2, 90, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

This sequence is idempotent, meaning a(a(n)) = a(n) for all n.

All terms belong to A289509.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Wikipedia, Idempotence

Index entries for sequences computed from indices in prime factorization

MATHEMATICA

f[n_]:=If[n==1, 1, With[{pms=Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]}, Times@@Prime/@(pms/GCD@@pms)]];

Table[f[n], {n, 100}]

PROG

(PARI) A316437(n) = if(1==n, 1, my(f = factor(n), pis = apply(p -> primepi(p), f[, 1]~), es = f[, 2]~, g = gcd(pis)); factorback(vector(#f~, k, prime(pis[k]/g)^es[k]))); \\ Antti Karttunen, Aug 06 2018

CROSSREFS

Cf. A000720, A056239, A289508, A289509, A290103, A296150, A316430, A316431, A316432, A316438.

Sequence in context: A331580 A320389 A046801 * A137502 A318885 A307088

Adjacent sequences:  A316434 A316435 A316436 * A316438 A316439 A316440

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 03 2018

EXTENSIONS

More terms from Antti Karttunen, Aug 06 2018

STATUS

approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)