A250478 Number of times prime(n) occurs as the least prime factor among numbers 1 .. prime(n)^4: a(n) = A078898(A030514(n)).

8, 14, 42, 92, 305, 455, 944, 1238, 2085, 3995, 4710, 7757, 10273, 11558, 14742, 20701, 28019, 30444, 39680, 46534, 49856, 62350, 71394, 86977, 111352, 124421, 130649, 145076, 151939, 167759, 236113, 257098, 291830, 302611, 370060, 382610, 427214, 475078

Offset: 1

Author

Antti Karttunen, Dec 14 2014

Keywords

• nonn
• changed

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..100

Crossrefs

Column 8 of A249822.

Cf. also A250474 (column 4), A250477 (column 6).

Cf. A002110, A030514, A030078, A078898.

Programs

PARI

allocatemem(234567890);
A002110(n) = prod(i=1, n, prime(i));
A250478(n) = { my(p3); p3 = (prime(n)^3); sumdiv(A002110(n-1), d, (moebius(d)*(p3\d))); };
for(n=1, 23, print1(A250478(n),", "));

Scheme

(define (A250478 n) (A078898 (A030514 n)))

Formula

a(n) = A078898(A030514(n)).

a(1) = 1, a(n) = sum_{d | A002110(n-1)} moebius(d) * floor(prime(n)^3 / d). [Follows when A030514, prime(n)^4 is substituted to the similar formula given for A078898. Here A002110(n) gives the product of the first n primes. Because the latter is always squarefree, one could use here also Liouville's lambda (A008836) instead of Moebius mu (A008683).]

Extensions

More terms from Jon E. Schoenfield, Dec 14 2014