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

1,1

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

Crossrefs

Cf. A056239, A074761, A110295, A143773, A237984, A289508, A289509, A290103, A296150, A316413, A316428, A316430, A316431.

Sequence in context: A279897 A336131 A095967 * A337639 A047161 A318193

Adjacent sequences: A316426 A316427 A316428 * A316430 A316431 A316432

Keyword

nonn,easy

Author

Gus Wiseman, Jul 02 2018

Status

approved