A324193 a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, dA297167(d)).

0, 1, 1, 2, 1, 6, 1, 6, 3, 10, 1, 54, 1, 14, 15, 30, 1, 90, 1, 150, 21, 22, 1, 1350, 5, 26, 15, 294, 1, 2250, 1, 210, 33, 34, 35, 6750, 1, 38, 39, 5250, 1, 6174, 1, 726, 375, 46, 1, 66150, 7, 350, 51, 1014, 1, 3150, 55, 16170, 57, 58, 1, 1181250, 1, 62, 735, 2310, 65, 23958, 1, 1734, 69, 17150, 1, 1653750, 1, 74, 525, 2166, 77, 39546, 1, 404250, 105

Offset: 1

Author

Antti Karttunen, Feb 20 2019

Keywords

• nonn

Comments

An auxiliary sequence for defining A300827, which is the restricted growth sequence transform of this sequence. A324202 is a similar sequence, but is not limited to the proper divisors of n, and in contrast to this, also finds the least prime signature representative (A046523) of the product formed.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A001221, A001222, A007913, A061395, A087207, A297167, A300827 (rgs-transform), A324120, A324180.

Cf. also A324202.

Programs

PARI

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A324193(n) = { my(m=1); if(n<=2, n-1, fordiv(n, d, if((d>1)&(dA297167(d)))); (m)); };

Formula

a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, dA297167(d)).

For all n > 0:

A001222(a(n)) = A000005(n)-2.

A001221(A007913(a(n))) = A324120(n).

A087207(A007913(a(n))) = A324180(n).