A316431 Least common multiple divided by greatest common divisor of the integer partition with Heinz number n > 1.

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

Offset: 2

Author

Gus Wiseman, Jul 02 2018

Keywords

• nonn
• look

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A005117, A056239, A074761, A289508, A289509, A290103, A296150, A316429, A316430, A316437.

Programs

Mathematica

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

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

Formula

a(n) = A290103(n)/A289508(n).

a(n) = a(A005117(n)). - David A. Corneth, Sep 06 2018

Extensions

More terms from Antti Karttunen, Sep 06 2018