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.

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

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: A378447 A046801 A348717 * 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