A385718 -id:A385718 - cp's OEIS frontend

A385586 Primes p such that there exists prime q < p such that sigma(p+1) = sigma(q+1) = p + q.

37, 34687, 65587, 2089951, 8161477, 8340613, 18927067, 25855567, 64346413, 95150203, 238973101, 257658061, 277743397, 322210813, 349883707, 578403913, 704710543, 1121445337, 1654635937, 1741780693, 1804380007, 1963734061, 2346701941, 2360966173, 2720420707, 3232299517, 4343250181, 4925742973, 8085909913, 9044601133

Offset: 1

S. I. Dimitrov, Jul 03 2025

nonn

The primes p and q form a P(1, 1)-amicable pair. See Dimitrov link.

			(23, 37) is such a pair because sigma(23+1)=sigma(37+1) = 23 + 37.

S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Cf. A000203, A000040, A063990, A008333, A259180, A385718.

Subequence of A385705.

upto(n) = {
    res = List();
    forprime(p = 2, n,
        s = sigma(p+1);
        q = s - p;
        if(q < p && isprime(q) && sigma(q+1) == s,
            print([p, q]);
            listput(res, p);
        );
    ); res
} \\ David A. Corneth, Jul 03 2025

More terms from David A. Corneth, Jul 03 2025

A385739 Primes p such that there exists a prime q < p such that sigma(q-1) = sigma(p+1) = p + q.

Original entry on oeis.org

5563, 203431, 389923, 901423, 5495263, 7418863, 28128367, 188953969, 210627577, 392753209, 402877087, 505757683, 619418689, 2549153611, 2580356851, 3953660383, 5692944349, 6806206831, 6894059071, 7082199673, 10058113363, 11307503629, 12601725943, 12615171649

Offset: 1

S. I. Dimitrov, Jul 08 2025

The primes q and p form a P(-1, 1)-amicable pair. Apparently (q-1, p+1) is an amicable pair A259180.

			(5021, 5563) is such a pair because sigma(5021-1) = sigma(5563+1) = 5021 + 5563.

S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Cf. A000040, A000203, A063990, A008333, A259180, A385586, A385718.

a(5)-a(13) from Michel Marcus, Jul 08 2025

a(14)-a(24) from Giorgos Kalogeropoulos, Jul 14 2025

A385740 Primes p such that there exists a prime q < p such that sigma(p-1) = sigma(q-1) = p + q.

Original entry on oeis.org

1163, 7583, 17099, 48857, 65963, 172859, 5408423, 6804047, 19247087, 73162367, 77695043, 109775657, 109871933, 116464757, 160454717, 175031957, 175288493, 218543393, 268382183, 303220769, 379299989, 705800723, 823155779, 889218389, 967371143, 1100618483, 1242282407, 1701133163

Offset: 1

S. I. Dimitrov, Jul 08 2025

The primes q and p form a P(-1, -1)-amicable pair. See Dimitrov link.

			(853, 1163) is such a pair because sigma(853-1) = sigma(1163-1) = 853 + 1163.

S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Cf. A000040, A000203, A063990, A008333, A259180, A385586, A385718, A385739.

a(6)-a(25) from Michel Marcus, Jul 08 2025

a(26)-a(28) from Giorgos Kalogeropoulos, Jul 14 2025

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A385586 Primes p such that there exists prime q < p such that sigma(p+1) = sigma(q+1) = p + q.

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A385739 Primes p such that there exists a prime q < p such that sigma(q-1) = sigma(p+1) = p + q.

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A385740 Primes p such that there exists a prime q < p such that sigma(p-1) = sigma(q-1) = p + q.

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Examples

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Extensions