A326148 - OEIS

A326148

Odd numbers > 1, not powers of primes, for which A326147(n) is equal to abs(A326146(n)).

15, 91, 207, 703, 847, 1023, 1891, 2701, 2725, 5551, 12403, 15043, 18721, 19359, 38503, 49141, 79003, 88831, 104653, 146611, 148951, 188191, 218791, 226801, 269011, 286903, 346957, 385003, 497503, 597871, 665281, 721801, 736291, 765703, 873181, 954271, 1056331, 1207359, 1314631, 1345873, 1373653, 1537381, 1755001

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OFFSET

1,1

COMMENTS

Odd numbers > 1, not powers of primes, for which A326146(n) [= (sigma(n)-A020639(n)-n)] is not zero and divides n-A020639(n).

Question: Are any of these terms present also in A326064 and A326074? None of the first 519 terms are. If such intersections are empty, then there are no odd perfect numbers.

Of the first 519 terms, 485 are semiprimes.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..519; all terms < 2^31

Index entries for sequences where any odd perfect numbers must occur

PROG

(PARI)

A020639(n) = if(1==n, n, factor(n)[1, 1]);

A326146(n) = (sigma(n)-A020639(n)-n);

A326147(n) = gcd(n-A020639(n), sigma(n)-A020639(n)-n);

isA326148(n) = if((n>1)&&(n%2)&&!isprimepower(n), my(s=factor(n)[1, 1], t=n-s, u=sigma(n)-s-n); (u && !(t%u)), 0);

CROSSREFS

Cf. A020639, A046666, A326064, A326074, A326146, A326147.