A377986 - OEIS

A377986

Number of integers k, with bigomega(k) > 2, whose arithmetic derivative (A003415) is equal to n!, the n-th factorial.

0, 0, 0, 1, 1, 1, 2, 1, 2, 6, 0, 4, 4, 3, 7

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OFFSET

1,7

COMMENTS

The solutions (composite, nonsemiprime antiderivatives of n!) are given in A377987.

LINKS

FORMULA

a(n) = Sum_{k=1..A002620(n!)} [A003415(k) = n! and A001222(k) > 2], where [ ] is the Iverson bracket.

a(n) = A376410(n) - A062311(n).

EXAMPLE

See the examples in A377987.

PROG

(PARI)

A002620(n) = ((n^2)>>2);

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A377986(n) = { my(g=n!); sum(k=1, A002620(g), (bigomega(k)>2) && (A003415(k)==g)); };

(PARI) A377986(n) = AntiDeriv(n!, 2, "a_terms_for_A377987_unsorted.txt"); \\ The rest of the program is given in A376410.

CROSSREFS

Row lengths of irregular triangle A377987.

KEYWORD

nonn,hard,more,new

AUTHOR

STATUS

approved