A342555 2*a(n) is the start of 3 consecutive numbers (even-odd-even) that are sums of divisors, i.e., terms of A000203.

3, 6, 15, 19, 63, 153, 199, 255, 423, 480, 511, 546, 861, 1111, 1189, 1400, 1770, 1875, 1935, 1995, 2047, 2556, 3475, 3619, 4005, 4095, 4920, 5151, 5215, 6649, 8046, 8191, 8646, 8749, 9765, 11175, 11199, 14028, 14197, 15391, 15427, 15470, 16383, 19494, 25878, 26557, 26799

Offset

1,1

Comments

There exists one exceptional case of 4 consecutive numbers 12, 13, 14, 15, where 13 would start an odd-even-odd progression.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..1000

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems: invphi.gp, Oct. 2005.

Jeppe Stig Nielsen, List of numbers with divisor sum k, k<=10000.

Example

a(1) = 3, because 2*3 = 6 is the start of the first occurrence of a row of 3 consecutive numbers, all of which are in A000203. 6 = sigma(5), 7 = sigma(4), 8 = sigma(7).
a(2) = 6: 2*6 = 12 = sigma(6) = sigma(11), 13 = sigma(9), 14 = sigma(13). 15 = sigma(8), which would be at the end of the row 13, 14, 15, is excluded by the even-odd-even condition.
a(3) = 15: 2*15 = 30 = sigma(29), 31 = sigma(16) = sigma(25), 32 = sigma(21) = sigma(31).
See Jeppe Stig Nielsen's list for more examples.

Prog

(PARI) a342555(nterms) = {my(N=vector(3, i, invsigmaNum(i+1)), n=0, k=4); while(n<=nterms, if(vecmin(N)>0 && !(k%2), print1((k-2)/2, ", "); n++); k++; N[1+k%3] = invsigmaNum(k))}; \\ see Alekseyev link for invsigmaNum()
a342555(46)

Crossrefs

Cf. A000203, A085790, A342560.

Sequence in context: A276546 A265486 A060304 * A075868 A162335 A289296

Adjacent sequences: A342552 A342553 A342554 * A342556 A342557 A342558

Keyword

nonn

Author

Hugo Pfoertner, May 14 2021

Status

approved