

A316431


Least common multiple divided by greatest common divisor of the integer partition with Heinz number n > 1.


17



1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 6, 1, 1, 2, 1, 3, 2, 5, 1, 2, 1, 6, 1, 4, 1, 6, 1, 1, 10, 7, 12, 2, 1, 8, 3, 3, 1, 4, 1, 5, 6, 9, 1, 2, 1, 3, 14, 6, 1, 2, 15, 4, 4, 10, 1, 6, 1, 11, 2, 1, 2, 10, 1, 7, 18, 12, 1, 2, 1, 12, 6, 8, 20, 6, 1, 3, 1, 13, 1, 4, 21, 14, 5, 5, 1, 6, 6, 9, 22, 15, 24, 2, 1, 4, 10, 3, 1, 14, 1, 6, 12
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OFFSET

2,5


COMMENTS

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


LINKS

Antti Karttunen, Table of n, a(n) for n = 2..65537
Index entries for sequences computed from indices in prime factorization
Index entries for sequences related to Heinz numbers


FORMULA

a(n) = A290103(n)/A289508(n).
a(n) = a(A005117(n)).  David A. Corneth, Sep 06 2018


EXAMPLE

63 is the Heinz number of (4,2,2), which has LCM 4 and GCD 2, so a(63) = 4/2 = 2.
91 is the Heinz number of (6,4), which has LCM 12 and GCD 2, so a(91) = 12/2 = 6.


MATHEMATICA

Table[With[{pms=Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]]}, LCM@@pms/GCD@@pms], {n, 2, 100}]


PROG

(PARI) A316431(n) = if(1==n, 1, my(pis = apply(p > primepi(p), factor(n)[, 1]~)); lcm(pis)/gcd(pis)); \\ Antti Karttunen, Sep 06 2018


CROSSREFS

Cf. A005117, A056239, A074761, A289508, A289509, A290103, A296150, A316429, A316430, A316437.
Sequence in context: A120454 A321648 A330755 * A319567 A076511 A280688
Adjacent sequences: A316428 A316429 A316430 * A316432 A316433 A316434


KEYWORD

nonn,look


AUTHOR

Gus Wiseman, Jul 02 2018


EXTENSIONS

More terms from Antti Karttunen, Sep 06 2018


STATUS

approved



