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A316429
Heinz numbers of integer partitions whose length is equal to their LCM.
11
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
1,1
COMMENTS
A110295 is a subsequence.
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10822 (Terms <= 5 * 10^11)
EXAMPLE
3750 is the Heinz number of (3,3,3,3,2,1), whose length and lcm are both 6.
MATHEMATICA
Select[Range[2, 200], PrimeOmega[#]==LCM@@Cases[FactorInteger[#], {p_, k_}:>PrimePi[p]]&]
PROG
(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
KEYWORD
nonn,easy
AUTHOR
Gus Wiseman, Jul 02 2018
STATUS
approved