A324193 a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, d<n} prime(1+A297167(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

1,4

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

Formula

a(1) = 0; for n > 1, a(n) = Product_{d|n, d>1, d<n} prime(1+A297167(d)).

For all n > 0:

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

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

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

Prog

(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)&(d<n), m *= prime(1+A297167(d)))); (m)); };

Crossrefs

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

Cf. also A324202.

Sequence in context: A166120 A318256 A324370 * A364829 A264859 A007956

Adjacent sequences: A324190 A324191 A324192 * A324194 A324195 A324196

Keyword

nonn

Author

Antti Karttunen, Feb 20 2019

Status

approved