A316429 Heinz numbers of integer partitions whose length is equal to their LCM.
2, 6, 9, 20, 50, 56, 84, 125, 126, 176, 189, 196, 240, 294, 360, 416, 441, 540, 600, 624, 686, 810, 900, 936, 968, 1029, 1040, 1088, 1215, 1350, 1404, 1500, 1560, 2025, 2106, 2250, 2340, 2401, 2432, 2600, 2704, 3159, 3375, 3510, 3648, 3750, 3900, 4056, 5265
Offset: 1
Examples
3750 is the Heinz number of (3,3,3,3,2,1), whose length and lcm are both 6.
Links
- David A. Corneth, Table of n, a(n) for n = 1..10822 (Terms <= 5 * 10^11)
Crossrefs
Programs
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Mathematica
Select[Range[2,200],PrimeOmega[#]==LCM@@Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]]&] -
PARI
heinz(n) = my(f=factor(n), pr=f[,1]~,exps=f[,2], res=vector(vecsum(exps)), t=0); for(i = 1, #pr, pr[i] = primepi(pr[i]); for(j=1, exps[i],t++; res[t] = pr[i])); res is(n) = my(h = heinz(n)); lcm(h)==#h \\ David A. Corneth, Jul 05 2018
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