A329346 a(n) = A322356(A324886(n)).

1, 1, 1, 1, 1, 1, 1, 5, 7, 1, 1, 1, 1, 1, 1, 5, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 7, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 7, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 19, 1, 1, 1, 1, 13, 1, 7, 1, 1, 13, 1, 1, 1, 1, 1, 7, 1, 1, 13, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 7, 1, 13, 1, 13, 1, 1, 1, 1, 13

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial base

Index entries for sequences related to primorial numbers

Formula

a(n) = A322356(A324886(n)).

Example

For n = 128 = 2^7, A108951(128) = A034386(2)^7 = 128. As 128 = 4 * 30 + 1*6 + 1* 2, A276086(128) = 36015 = 7^4 * 5^1 * 3^1, and there are two such primes that both p and p-2 divide n, and p-2 is also prime, namely, 7 and 5, thus a(128) = 7*5 = 35. This is also the first occurrence of composite number in this sequence.

Prog

(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A324886(n) = A276086(A108951(n));
A322356(n) = { my(f = factor(n), m=1); for(i=1, #f~, if(isprime(f[i, 1]+2)&&!(n%(f[i, 1]+2)), m *= (f[i, 1]+2))); (m); };
A329346(n) = A322356(A324886(n));

Crossrefs

Cf. A002110, A034386, A108951, A276086, A324886, A329040, A322356, A329343, , A329344, A329347, A329348.

Sequence in context: A133412 A111833 A011378 * A258716 A195300 A019697

Adjacent sequences: A329343 A329344 A329345 * A329347 A329348 A329349

Keyword

nonn

Author

Antti Karttunen, Nov 11 2019

Status

approved