cp's OEIS Frontend

A336568 Numbers that are not a product of two numbers each having distinct prime multiplicities.

%I A336568 #17 Jul 08 2022 16:06:51
%S A336568 30,42,66,70,78,102,105,110,114,130,138,154,165,170,174,182,186,190,
%T A336568 195,210,222,230,231,238,246,255,258,266,273,282,285,286,290,310,318,
%U A336568 322,330,345,354,357,366,370,374,385,390,399,402,406,410,418,420,426,429
%N A336568 Numbers that are not a product of two numbers each having distinct prime multiplicities.
%C A336568 First differs from A007304 and A093599 in having 210.
%C A336568 First differs from A287483 in having 222.
%C A336568 First differs from A350352 in having 420.
%C A336568 A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization, so a number has distinct prime multiplicities iff all the exponents in its prime signature are distinct.
%e A336568 Selected terms together with their prime indices:
%e A336568    660: {1,1,2,3,5}
%e A336568    798: {1,2,4,8}
%e A336568    840: {1,1,1,2,3,4}
%e A336568   3120: {1,1,1,1,2,3,6}
%e A336568   9900: {1,1,2,2,3,3,5}
%t A336568 strsig[n_]:=UnsameQ@@Last/@FactorInteger[n]
%t A336568 Select[Range[100],Function[n,Select[Divisors[n],strsig[#]&&strsig[n/#]&]=={}]]
%Y A336568 A336500 has zeros at these positions.
%Y A336568 A007425 counts divisors of divisors.
%Y A336568 A056924 counts divisors greater than their quotient.
%Y A336568 A074206 counts strict chains of divisors from n to 1.
%Y A336568 A130091 lists numbers with distinct prime multiplicities.
%Y A336568 A181796 counts divisors with distinct prime multiplicities.
%Y A336568 A336424 counts factorizations using A130091.
%Y A336568 A336422 counts divisible pairs of divisors, both in A130091.
%Y A336568 A327498 is the maximum divisor with distinct prime multiplicities.
%Y A336568 A336423 counts chains in A130091, with maximal version A336569.
%Y A336568 A336571 counts divisor sets using A130091, with maximal version A336570.
%Y A336568 Cf. A001055, A002033, A098859, A124010, A167865, A253249, A336420.
%K A336568 nonn
%O A336568 1,1
%A A336568 _Gus Wiseman_, Aug 06 2020