A379216 - OEIS

A379216

Difference 2*k - A003961(k) computed for k for which this difference divides difference (A003961(k)-sigma(k)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

1, 1, 1, -1, -3, 3, -1, 1, 1, -43, 1, 5, 19, -1, -7, -5, 1, -2005, 1, -1, 149, -193, -1, -3, -79243, 1243, 1253, -7, 51, 581, -1, 3093, 1, 155491, 919, 1, -1, 15833, -877, -4295498497, 5129369, 31, 5779339, -69187, -29, 6745, 1, 181, 1, 69197, -397, -117433, -101, -1, 1, 2759, 1, -29479, 1, -5626288431709, 29669, -1, -132239, -1, -1, 14591, -2267959, -3187, 787250461

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OFFSET

1,5

COMMENTS

Among the initial 69 terms, there are eleven +1's and eleven -1's. The former correspond in A378980 with those of its terms that are in A048674 (1, 2, 3, 25, 26, 33, 93, 1034, ...), while the latter here correspond in A378980 with those of its terms that are in A348514 (4, 10, 57, 1054, 2626, ...).

LINKS

Table of n, a(n) for n=1..69.

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

FORMULA

a(n) = -A252748(A378980(n)).

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

A378981(n) = ((A003961(n)-sigma(n))%((2*n)-A003961(n)));

is_A378980(n) = !A378981(n);

for(n=1, 2^25, if(is_A378980(n), print1((2*n)-A003961(n), ", ")));