cp's OEIS Frontend

A359360 Length times minimum part of the integer partition with Heinz number n. Least prime index of n times number of prime indices of n.

%I A359360 #8 Dec 28 2022 15:42:39
%S A359360 0,1,2,2,3,2,4,3,4,2,5,3,6,2,4,4,7,3,8,3,4,2,9,4,6,2,6,3,10,3,11,5,4,
%T A359360 2,6,4,12,2,4,4,13,3,14,3,6,2,15,5,8,3,4,3,16,4,6,4,4,2,17,4,18,2,6,6,
%U A359360 6,3,19,3,4,3,20,5,21,2,6,3,8,3,22,5,8,2
%N A359360 Length times minimum part of the integer partition with Heinz number n. Least prime index of n times number of prime indices of n.
%C A359360 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A prime index of n is a number m such that prime(m) divides n.
%F A359360 a(n) = A001222(n) * A055396(n).
%e A359360 The partition with Heinz number 7865 is (6,5,5,3), so a(7865) = 4*3 = 12.
%t A359360 Table[PrimeOmega[n]*PrimePi[FactorInteger[n][[1,1]]],{n,100}]
%o A359360 (PARI) a(n) = if (n==1, 0, my(f=factor(n)); bigomega(f)*primepi(f[1, 1])); \\ _Michel Marcus_, Dec 28 2022
%Y A359360 Difference of A056239 and A359358.
%Y A359360 The opposite version is A326846.
%Y A359360 A055396 gives minimum prime index, maximum A061395.
%Y A359360 A112798 list prime indices, length A001222, sum A056239.
%Y A359360 A243055 subtracts the least prime index from the greatest.
%Y A359360 A358195 gives Heinz numbers of rows of A358172, even bisection A241916.
%Y A359360 Cf. A006141, A124010, A246277, A268192, A316413, A325352, A326836, A326837, A326844, A355534, A356958.
%K A359360 nonn
%O A359360 1,3
%A A359360 _Gus Wiseman_, Dec 28 2022