A289623 a(n) = A055396(A048673(n)).

0, 1, 2, 3, 1, 1, 1, 1, 6, 5, 4, 9, 2, 7, 1, 13, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 16, 8, 1, 2, 10, 2, 30, 2, 3, 14, 3, 1, 23, 1, 17, 1, 1, 2, 4, 18, 1, 1, 4, 1, 1, 1, 35, 1, 15, 11, 1, 1, 1, 1, 3, 1, 1, 1, 1, 21, 1, 12, 1, 1, 1, 2, 1, 1, 1, 1, 1, 65, 3, 2, 1, 19, 20, 1, 1, 4, 56, 1, 32, 2, 1, 2, 1, 2, 1, 38, 6

Offset

1,3

Comments

From the scatter plot it can be seen that the terms are grouped into two distinct populations by their magnitude, with significant gap between them.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = A055396(A048673(n)).

Prog

(PARI)
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ This function from Michel Marcus
A048673(n) = (A003961(n)+1)/2;
A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015
A289623(n) = A055396(A048673(n));

Crossrefs

Cf. A048673, A055396, A246263 (the positions of ones).

Cf. also A278224, A286582, A286583, A286584, A286586.

Sequence in context: A308638 A356320 A207572 * A086195 A086197 A139336

Adjacent sequences: A289620 A289621 A289622 * A289624 A289625 A289626

Keyword

nonn,look

Author

Antti Karttunen, Jul 16 2017

Status

approved